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OpenGL Programming/Basics/3DObjects

OpenGL is a powerful graphics library that allows you to create 3D graphics in C++. In this tutorial, we will be discussing how to draw a simple 3D object in OpenGL and C++. We will be using the GLUT library for this tutorial, which provides a set of tools for creating simple OpenGL applications.

Prerequisites
Before we get started, make sure you have the following software installed:

 * An IDE such as Visual Studio or Code::Blocks
 * The GLUT library
 * OpenGL headers and libraries

Setting Up
To get started, create a new C++ project in your IDE and include the necessary OpenGL and GLUT headers. Here's an example: Next, we'll define some variables for our 3D object: We'll use these variables to manipulate the position and orientation of our object.

Drawing a Simple 3D Object
Let's start by drawing a simple cube. We'll use the  function to create the cube, and   and   to position and orient it. The  function clears the color and depth buffers, and   and   set the current matrix mode and load the identity matrix, respectively. The  and   functions are used to position and orient the cube, and the   function is used to draw the cube. Finally,  is used to swap the front and back buffers.

We'll also need to set up the window and OpenGL context in the  function: The   function initializes GLUT, and   sets up the display mode. sets the window size, and  creates the window. enables depth testing. Finally,  and   set the display and idle functions, respectively, and   enters the GLUT event processing loop.

Conclusion
In this tutorial, we learned how to draw a simple 3D object in OpenGL and C++. We used the GLUT library to set up the window and OpenGL context, and we used  and   to position and orient the cube. We also discussed how to enable depth testing to ensure that objects are rendered correctly based

title: OpenGL Programming/Basics/3DObjects


text:
Kittypet's Guide To Warrior Cats/Authors & Contributors

This list is updated automatically by AuthorsAndContributorsBot. Please do not update it manually.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Talk:LMIs in Control/Discrete-Time Algebraic Riccati Inequality (DARE)

Incorrect statements
This page presents completely incorrect results. The left-hand side of the Riccati inequality should negative semidefinite and not positive semidefinite. It is immediate to find examples for which the computed control law does not stabilize the system. The provided code shows that. In this regard, this page should be removed. 2A04:EE41:6:927B:80FF:E28F:B1D3:82A5 (discuss) 09:17, 20 February 2023 (UTC)


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Minecraft/Boss Fight: Ender Dragon

The Ender Dragon is the final boss in the game, and for some, the toughest (the warden is not considered a boss). This page will guide you through defeating the dragon, and claim the rewards.

Getting to The End

 * Required items: 14 - 16 eyes of ender
 * Recommended: good gear, diamond at least, with max level feather falling enchant; golden apples and healing potions, a bow/crossbow with at least 16 - 60 arrows (depending on your aim); 64 logs, as backup materials; a bed; as many ender pearls as you can get
 * Optional, only if you want to maximize reward: at least 30 glass bottles; as many firework rockets as possible

You will first need to throw the eye of ender, and see where it points. Pick the eye up (although there is a 1 in 8 chance for it to be destroyed, in which case, skip that part), and carry on walking in the direction the eye traveled.

Every few hundred blocks, throw the eye again, just to make sure you're going in the correct direction. Always make sure to pick it up, you will need at least 11 to actually open the portal to the end.

If it goes underground, you are almost there. Just dig the ground where it fell into, and go down, until you see stone bricks. Enter the structure, and search for the portal room. You know you found it when you can see a mob spawner, 3 small pools of lava, and a stairway up to a ring of yellow blocks.

Those yellow blocks are portal frames. To activate the portal, each frame must contain an eye. To put the eye in the frame, interact with it while holding an eye of ender.

Once each eye is in, the portal will activate. Before you enter, seal off the portal room, place the bed somewhere - do not place it directly under the portal or you will be trapped in the end forever - and set your spawn to it. If you can make an ender chest, do so, and place it. Prepare to fight, and enter the portal.

Defeating the dragon
To kill the ender dragon, you first need to destroy at least 6 of the 8 ender crystals at the top of each obsidian pillar. Destroying more after the first 6 is unnecessary, but makes the fight easier.

The best way to destroy the crystals without exposing yourself to serious harm is to shoot them with arrows. If you cannot hit them, climb up, and destroy the crystal by hitting it. Make sure to have your shield out when you do, since the crystals explode with a force stronger than a charged creeper.

After enough crystals have been destroyed, go to the center pedestal, and wait for the dragon. Make sure to stand inside it. When the dragon comes down, attack it with your strongest melee weapon (arrows bounce off of it if it is on the pedestal). When it dies, quickle jump out of the pedestal. Feel free to watch the rays of light until the dragon disappears.

Maximizing the rewards - during fight
When the dragon uses the fireball attack, it creates a damaging purple cloud. Scoop this up with an empty glass bottle to get dragon's breath. This can be brewed with splash potions to make lingering potions.

Maximizing the rewards - post victory
When the dragon dies, an egg is revealed on the central pedestal. If you hit it, it just teleports away. Instead, let it teleport on a breakable block, like end stone, mine two blocks under it and place a torch. Then break the block below the egg. The egg should fall onto the torch and break, so that you can pick it up. Buttons and slabs also work.

Make sure to put the egg in the ender chest back in the overworld, along with any treasres. To return, just jump into the pedestal where you found the egg. After putting it in your ender chest, return to the end.

Look for a floating bedrock structure (found near the edge), and throw an ender pearl in to the central black block. Do not move until everything is loaded, as you will likely be only a step away from falling into the void. Carefuly move to firmer ground, making sure to mark a trail of some sort to make sure you don't get lost.

What you are looking for is an end city. A large tower made of purple blocks. Once you enter it, make sure to kill all the shulkers (they look like purple blocks, and shoot projectiles at you that make you levitate into the air), preferably with a sword enchanted with looting III. The shulker shells they drop can be crafted into shulker boxes.

Keep exploring the whole city, looting chests and hunting shulkers.

If you find a ship, enter it and go below the deck. In an item frame is an elytra, which allows you to fly in survival when equipped instead of a chestplate.

Aim to get at least 24 shulker shells, which is enough for 12 shulker boxes.

Respawning the dragon
You can respawn the dragon by crafting four end crystals, and placing one on each of the four sides of the central pedistal in the end. This will respawn the ender dragon, allowing you to refight it, collect more dragon's breath, or get more XP for enchanting. Doing this will not give another dragon egg, and unless you have taken the egg from the pedestal, the egg will be destroyed, so be careful.

title: Minecraft/Boss Fight: Ender Dragon


text:
Chess Opening Theory/1. e4/1...e5/2. Qh5/2...Nc6/3. Bc4/3...g6/4. Qf3/4...Nf6/5. Nc3

= Parham Attack =

5. Nc3
Moving the knight to c3 seems natural, since it develops the knight and prevents Black's d-pawn advance. However, this move can be considered a mistake. This is because Black can gain a tempo by playing Nd4!, moving to an outpost which threatens to win the queen while also threatening to fork white’s pieces at the same time.


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Fractals/target set

=Definition=

Dynamical plane is divided into
 * Fatou set
 * Julisa set

Fatou set consist of one or more basins of attraction to the attractor.

Each basin of attraction has one or more critical points which fall into periodic obit ( attractor)

Target set
 * is a trap for forward orbit
 * is a set which captures any orbit tending to attractor (limit set = attracting cycle = fixed / periodic point).

=Types=

Criteria for classifications: one can divide it according to :
 * attractors ( finite or infinite)
 * dynamics ( hyperbolic, parabolic, elliptic )
 * shape ( bailout test)
 * destination
 * decomposition of target set: binary decomposition ( BDM), angular decomposition,

For infinite attractor

 * Target set $$T\,$$ is an arbitrary set on dynamical plane containing infinity and not containing points of Filled-in Fatou sets.
 * For escape time algorithms target set determines the shape of level sets and curves. It does not do it for other methods.
 * For escaping to infinity points ( basin of infinity = exterior of Julia set) it is  exterior of circle with center at origin $$z = 0 \,$$ and radius =ER :

$$T_{ER}=\{z:abs(z) > ER \} \,$$

Radius is named escape radius ( ER ) or bailout value. Radius should be greater than 2.

Infinity:
 * for polynomials infinity is superattracting fixed point. So in the exterior of Julia set (basin of attraction of infinity) the dynamics is the same for all polynomials. Escaping test ( = bailout test) can be used as a first universal tool.
 * for rational maps infinity is not a superattrating fixed point. It may be periodic point or not.

For finite attractors

For finite attractors see: target set by basin

See :
 * Internal Level Sets
 * Binary decomposition
 * Tessellation of the Interior of Filled Julia Sets by Tomoki KAWAHIRA

by the dynamics

Here
 * $$ z_n $$ is the last iteration of critical orbit
 * $$ center $$ is the center of the trap ( circle shape)
 * $$z_p$$ is periodc / fixed point ( alfa fixed point)

Trap is the circle with center $$ z = center $$ and  radius = AR

repeling case

 * Stability index = cabs(multiplier) > 1.0
 * periodc / fixed point ( alfa fixed point) is repelling = ther is no interior of Julia set

attracting but not supperattracting case

 * $$ z_n < z_p < z_p + AR $$ and all points are inside Julia set
 * $$ AR = z_p - z_n$$
 * Stabilitu index: 0.0 < cabs(multiplier) < 0.0

Elliptic case
For the elliptic dynamics, when there is a Siegel disc, the target set is an inner circle

Supperattracting case
Attractors:
 * Infinity is allways superattracting for forward iteration of polynomials. Target set here is an exterior of any shape containing all point of Julia set (and its interior)
 * finite asttractors can also be superattracting, when parameter c is a center ( nucleus) of hyperbolic component of Mandelbrot set

In case of forward iteration target set $$T\,$$ is an arbitrary set on dynamical plane containing infinity and not containing points of filled Julia set.

supperattracting case : here
 * $$ z_{cr} = z_p$$ so one have to set AR manually, like AR = 30*PixelWidth
 * Stabilitu index = cabs(multiplier) = 0.0
 * Center of attracting basin is $$ center = z_cr = z_p$$

Parabolic case: petal
In parabolic case trap can be for
 * drawing components of Julia set
 * BDM = parabolic checkerboard

In the parabolic case target set should be inside the petal

parabolic case for child period 1 and 2 the target set can have circle shape :
 * one should:
 * compute AR
 * change trap center to midpoint between attracting fixed point zp and the last iteration of critical orbit zn to get: $$ z_n < center < z_p$$
 * Stabilitu index cabs(multiplier) = 1.0
 * here $$ AR = \frac{z_p - z_n}{2}$$

Fof child periods > 2 petal can be triangle fragment of the circle around fixed point for the parent period.

by destination
It is important for parabolic case:
 * for Fatou basin ( color depends on the target set): circle around fixed point = trap for interior
 * for component of Fatou basin ( color proportional to to iteration modulo period) - triangle fragment of above circle = biggest triangle (zp, zprep, -zprep) = trap for components
 * for level set of Fatou basin ( color proportional to last iteration number ) = trap for components
 * for BDM or parabolic checkerboard : 2 smaller triangles (zp, zprecr, zcr) and (zp, zcr, -zprecr) = traps for BD

-zprecr zf     	    zcr zprecr

where
 * p is a period
 * zf = fixed point ( here period = 1)
 * zcr = critical point z=0
 * zprecr = precritical point = preimage of critical point: $$f^{-p}( z_{cr} )$$. Note that inverse function is multivalued so one should choose the proper preimage

by the shape

 * circle
 * square
 * Julia set
 * p-norm disk

Exterior of circle
This is typical target set. It is exterior of circle with center at origin $$z = 0 \,$$ and radius =ER:

$$T_{ER}=\{z:abs(z) > ER \} \,$$

Radius is named escape radius (ER) or bailout value.

Circle of radius=ER centered at the origin is: $$ \{z:abs(z) = ER \} \,$$

For escaping to infinity points ( basin of infinity = exterior of Julia set) it is  exterior of circle with center at origin $$z = 0 \,$$ and radius =ER :

$$T_{ER}=\{z:abs(z) > ER \} \,$$

Radius is named escape radius ( ER ) or bailout value. Radius should be greater than 2.

For finite attractors it is interior of the circle with center at periodic point

$$T_{AR}=\{z :abs(z - z_p) < AR \} \,$$

For parabolic periodic points
 * it is called a petal
 * petal is interior of the circle
 * center of petal circle is equal to midpoint between lat iteration and parabolic periodic point
 * parabolic periodic point belongs to Julia set

Exterior of square
Here target set is exterior of square of side length $$s\, $$ centered at origin

$$T_s=\{z: abs(re(z)) > s \mbox{or}  abs(im(z))>s \} \,$$

Julia sets
Escher like tilings is a modification of the level set method ( LSM/J). Here Level sets of escape time are different because targest set is different. Here target set is a scalled filled-in Julia set.

For more description see
 * Fractint : escher_julia
 * page 187 from The Science of fractal images by Heinz-Otto Peitgen, Dietmar Saupe, Springer

p-norm disk
See also
 * kf
 * DLD

=References=

title: Fractals/target set


text:
Kittypet's Guide To Warrior Cats/Print version

 =Books=

 =Characters=  =Locations=

 =Clan Terminology=

 =Authors & Contributors=


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Cookbook:Ramekin

A ramekin is a small, deep dish made of glass or stoneware. Ramekins are often used to serve individual portions of various foods, such as custards and other baked goods. They are typically heat-safe so that they may be used in the oven.

title: Cookbook:Ramekin


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Cookbook:Brush

A brush, sometimes also specifically referred to as a pastry brush or basting brush, is a paintbrush-like tool used to brush or coat foods. It is well-suited, for example, to tasks like brushing pastries and/or meats with butter, oil, egg wash, sauces, and more.

Composition
Pastry brushes come in various materials, with bristles made from natural boar hair, silicone, or nylon. Natural bristles are prized for their ability to hold liquids well, providing an even application, while silicone brushes are durable, easy to clean, and heat-resistant, making them suitable for a range of kitchen tasks.

title: Cookbook:Brush


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Cookbook:Skewer

A skewer is a long, thin, sharp strip of metal or wood. It is most commonly used to pierce foods in order to cook them, as with kebabs. It is also a handy tool for checking the doneness of baked goods by piercing them. Toothpicks or cocktail picks are small skewers made of wood and sometimes plastic.

title: Cookbook:Skewer


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Cookbook:Non-stick

Nonstick equipment, and particularly pans, refers to equipment that has been treated with a special coating to reduce or prevent the sticking of food to the surface when cooking. This is usually achieved by coating the pan with teflon. Most nonstick equipment must not be heated beyond about 500°F (260°C) due to the degradation of the teflon into toxic compounds. Generally, metal tools should not be used on nonstick equipment since the metal is likely to scratch and damage the coating.

Steel and iron pans, when properly seasoned, will develop nonstick properties without the polymer coating. These are safe to use at high temperatures.

While nonstick pans are designed to reduce food sticking, some oil or parchment paper may still be needed to further reduce sticking, depending on the pan and the food being prepared.

title: Cookbook:Non-stick


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Cookbook:Cupcake Liner

Cupcake liners or pastry cases are small, often fluted cups made of parchment paper. They are used to line cupcake pans in order to facilitate the cakes' removal. They are also often used to hold finished pastries, making them easier to hold and transport. They can range from plain white to a variety of colors and patterns.

title: Cookbook:Cupcake Liner


text:
User talk:Connectpenguin

You cannot edit indefinitely due to disruptive editing. You may appeal this action with a reasonable argument by adding the text below.

--Xania   talk 00:50, 21 February 2023 (UTC)

title: User talk:Connectpenguin


text:
The Future of Leadership/Engagement Strategies in the Future of Work

Improving Hybrid/Remote Employee Engagement
Engaging employees is a consistent task that management must continuously adapt and with hybrid/remote employees it’s no different. The pandemic allowed for a new way of work to fully erupt. When the pandemic began, the number of remote workers doubled from 31% - 62% in only three weeks. As management and employees started to adjust to remote/hybrid work, fault lines were not only exposed but extrapolated. Some of the major fault lines that have affected engagement are communication, and connection.

Communication is one of the biggest challenges for hybrid/remote employees. Hybrid/remote employees tend to feel the need to over-communicate, over-perform, and over-sacrifice. A Microsoft work trend index report states communication has increased considerably, but with fewer boundaries, since the pandemic started. Hybrid/Remote employees tend to feel the need to prove that they are working. This can lead to performative actions like over-communicating via emails or instant work chats. Hybrid/Remote employees are also more likely to not establish boundaries, because of the feeling that they must prove they are working to the level of their in-person colleagues. Not only do employees feel the need to prove they are working, but they also have to work twice as hard to stay in the loop on projects. Hybrid/remote employees tend to be left out of minor decisions and exchanges, from their in-person colleagues. These minor correspondences can lead to hybrid/remote employees being left out of bigger conversations. These mishaps in communication are in part due to the lack of social connection hybrid/remote work produces. There are no longer the same in-person water cooler opportunities for hybrid/remote employees which can lead to them feeling disconnected and uninformed. A survey conducted by Economist found that respondents overwhelmingly indicated that poor communication at work can lead to stressful work environments, stalled careers missed performance goals, and lost sales”. Management must understand that hybrid/remote work is not equivalent to work-life balance. In order to properly engage hybrid/remote employees, management must prioritize communication and connection.

Following the quarantine of 2020 and the new “normal” environment, companies have been trying to determine trends in employee engagement and experience. Qualtrics, a leading experience management firm, determined four emerging trends based upon their Employee Experience (EX) Key Performance Indicators (KPIs) survey they provided to 16,000 companies in 2022:

 * 1) Instilling confidence you are running a successful ship is critical to your employee experience
 * 2) Employees have been operating at surge levels for years. Now, they’re reclaiming boundaries
 * 3) Bad processes and inefficient systems are fueling the risk of employee burnout
 * 4) Being employed isn’t just about having a job — it’s a part of a person’s value system

These trends are a good reflection of the current work force and signify a major change companies must face. Research suggests that managers should be actively engaging their employees by "re-recruiting" them. Re-recruiting should revolve around on how to keep current employees by discovering their motivation, compensation and professional development goals. Managers can choose to integrate these efforts into their annual employee assessments or to have these conversations casually throughout the year. Employees also want to connected to their company's mission, culture and values. "“Having a compelling mission, culture and values are critical when it comes to attracting and retaining top talent in a competitive job market — it is what differentiates each and every employer.” - Christian Sutherland-Wong, Glassdoor President and COO"

Improving Employee Engagement through Onboarding
Employee engagement has become a hot button topic in our post pandemic work environment, but what does it mean? Gallup defines employee engagement as the involvement and enthusiasm of employees in both their work and workplace. Employee engagement begins well before the first day of the job. A new hire’s experience on their first day sets the stage for the rest of their employment. Practices can help ensure that your onboarding process engages employees early and positively include things such as engaging employees early and often, creating a strong internal social network to engage employees, and engaging employees in your company’s cultural values.

Onboarding goes far beyond explaining the benefits package, desk location, and work schedule. Onboarding provides an opportunity to make new hires part of your organization’s community. Norming conversations that define the values, shared mission, and goals of the group provide clarity and direction. Discussions can range from what to wear to work to popular places to eat around the office. This is an opportunity to set the norms and expectations of behavior as it pertains to treating others well. In a report published by recruiting consultants, 22% of people surveyed reported that receiving a proper induction and onboarding influenced their decision to look for another job. Compared to 51% of employees admitting that a great onboarding experience motivated them to go “above and beyond.” Statistics like this help to illustrate the correlation between a good onboarding process and experience and employee engagement.

Improving Employee Engagement through Offboarding
The offboarding experience will be essential in the future of business. It allows companies one last chance to leave a lasting, positive impression on separating employees. Traditionally companies have invested significant resources in onboard and have neglected the offboarding process. Policies related to rehiring that served you well before might need to be revised to accommodate the new ways of business. Companies have created communities of previous employees, gig workers and boomerangs to create alumni networks to help in re-hiring talent, communication of jobs and partnerships.

Research also has found that when an employee leaves and human resources conducts an exit interview, that it is a good time to have informal conversations with the employees who are remaining. These “stay interviews” can help to corroborate information shared in exit interviews and measure the impact they will feel due to the departure of their colleague.


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Wikijunior:Famous Inventors/Inventors in Transportation/Clive Sinclair

Link to Clive Sinclair's Wikipedia entry

When, Where, and to whom was he or she born?
Clive Sinclair was born July 30, 1940.

He was born in Ealing, England.

What was his or her childhood like?
 Did You Know? Sinclair's father and grandfather were engineers; both had been apprentices at the shipbuilders Vickers.
 * He was also behind the Sinclair personal computer.
 * He invented the Micro Amplifier.
 * He was knighted in 1983.

Why did this person become interested in science?
He went for holiday jobs at electronic companies.

Where did this person go to school?
Sinclair attended Boxgrove Preparatory School, excelling in mathematics. Sinclair had little interest in sports and found himself out of place at school.

What problem did he or she uncover that needed solving?
At Solartron he inquired about the possibility of electrically propelled personal vehicles.

What solutions had already been tried that did not solve the problem? Why wasn't it working?
Bicycles, mopeds and cars did not offer personal electric transport. Lithium battery technology was not sufficiently developed.

What did this person invent that solved the problem?
The Sinclair C5.

How did the invention solve the problem?
It was a fared recumbent tricycle or velomobile with a battery electric motor.

How has this inventor changed people and the world?
He was ahead of his time. The Sinclair C5 predated escooters by several decades.

What happened to this inventor in the end?
Whilst Sinclair had anticipated 100,000 C5's would be sold in the first year, only 14,000 units were produced and 4,500 sold before the C5 line was terminated

If you could ask this inventor one question, what would you ask?
Could the C5 have succeeded with lithium battery and appropriate infrastructure?

If you could bring this inventor to today and tell him or her one thing, what would you tell him or her about the effect of his or her invention?
Escooters became popular.


text:
Chess Opening Theory/1. e4/1...e5/2. Qh5/2...Nc6/3. Bc4/3...g6/4. Qf3/4...Nf6/5. Nc3/5...Nd4

= Parham Attack =

5...Nd4!
Black threatens to fork White’s pieces while simultaneously putting pressure on the queen, thereby forcing it to retreat to its original square, resulting in a tempo gain. White has some options, white can respond with Qd1, which retreats the queen to it’s starting square while keeping pressure over the diagonals, or Qd3, which does not retreat the queen but instead protects the c2 pawn. However, playing Qd3 results in a loss of control over the diagonals.

White has a variety of moves to play here.

 * Qd1: Qd1 retreats the queen back to the square, saving white from being forked. This move is the best move to play in this position.

 * Qd3: An alternative to Qd1, but this lessens the control over the center.


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Basics of fine-art photography/Photo artist

Photo artist is a term used in relation to a creative person who has the ability to aesthetically display the world around him with the help of a special optical instrument and graphic editors. Figuratively speaking, "the poet of photography. Official sources sometimes use the synonym "master of artistic photography".

General information
Perhaps, in some countries of the world, this concept can serve as an official career, but in Russia (where the author of textbook comes from), such a profession is not documented. From which it follows: photo artist is a hobby, or an additional quality of a photographer.

A bit of reasoning
Of course, a wedding photographer (the optimal application of the specialty, if the goal is to generate income), will become more popular, putting in their work a grain of creativity, but can you qualify the results of his labors, as a kind of art? In order to answer this question, we will resort to allegory, considering two options.

 * 1) Boil the chicken and eat it.
 * 2) Before the meal, place the bird on a dish, decorating with herbs, vegetables, etc.

Point 2  differs from point 1  in that it has a creative component; perhaps some eaters would describe the work of a cook using the epithet "art" or "chef's art", but inherent in real art, a figurative understanding of reality is not even implied here, therefore the two concepts should be distinguished, both in this case and in the above example of the wedding photographer. These professions are merely adjusting to the demand of the population, whereas true art should exist only for the sake of art (and not for the satisfaction of the masses or individuals).

Think for yourself, decide for yourself...
What is the purpose of the above information? If the author, choosing the commercial path, shooting anniversaries, holidays and children's parties, will add a grain of artistry to his work, customers will appreciate it, which will be reflected in additional orders and, consequently, increase his (her) popularity and income. But one who gives preference to creative goals, for example engaging in experimental photography, will receive (at best) only positive feedback, which is unlikely to be accompanied by a material component; devoting himself to abstract photography, perhaps, he (she) will not be understood by society. In other words, creative research is at one's own expense.

Photographer / photo artist, similarities and differences
The photographer, usual, passively performs the tasks set by the client or the management; the photo artist can improvise, both with the post-processing of the resulting image and with the actions that precede the shooting. For the first, it is enough that the customer is satisfied with the result, the second can (and should) be in constant search.

How to become a photo artist?

 * 1) The first and necessary condition is the presence of artistic taste (or aesthetic consciousness).
 * 2) To begin with, it is enough to have the simplest camera: expensive models will distract from the goal.
 * 3) Choose one (or two) genres that appeal to you by carefully studying the textbook materials, in particular, all the enclosed photo examples.
 * 4) Determine for yourself the scope of work according to the chosen genre, having developed a concept.

But first of all you should decide whether you need it...

*** Below are examples: the first gallery contains works created by a photographer, the second — a photo artist. But everything presented to your attention is done ... by one author.


text: Template:Infobox song

title: Template:Infobox song


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Template:Infobox song/doc

Infobox person may be used to summarize information about a particular person, usually at the top of an article.

Usage
The infobox may be added by pasting the template as shown below into an article and then filling in the desired fields. Any parameters left blank or omitted will not be displayed.

Blank template with basic parameters

Blank template with all parameters

Parameters
Do not use all these parameters for any one person. The list is long to cover a wide range of people. Only use those parameters that convey essential or notable information about the subject. Any parameters left blank or omitted will not be displayed. If a data field has more than one parameter name which can be used, the preferred name is listed first in bold print.

Examples

title: Template:Infobox song/doc


text:
User:Djm-leighpark/common.js

$(document).ready(function {		alert("Are you sure you wish to continue editiing with abandoned account Djm-leighpark?"); });

title: User:Djm-leighpark/common.js


text:
Cookbook:Jigarthanda Milk

Jigarthanda (literally "heart-cooling") is a milk-based beverage to cool the body in summer. It is a kind of street food, and it originated in Madurai, India.

Jelly

 * 2 tbsp badam pisin (almond gum)
 * 1 cup (250 ml) water

Nannari/sarsaparilla syrup

 * 25 g Indian sarsaparilla root
 * 300 ml water
 * 150 g sugar

Jigarthanda ice cream

 * 1 ½ L full-fat milk
 * ¼ cup sugar
 * 2 tbsp sugar
 * 3 tbsp khova (milk solids)
 * ½ cup cream

Jigarthanda milk

 * 1 L full-fat milk
 * ¼ cup sugar

Jelly

 * 1) Wash and soak almond gum in the water for 3–4 hours or overnight. It should expand in size and form a jelly.
 * 2) Keep it in an airtight container in the fridge.

Nannari syrup

 * 1) Wash and crush the sarsaparilla root.
 * 2) Bring the water to a boil in a saucepan, then add the sarsaparilla.
 * 3) Reduce the heat, and simmer until the water is reduced by half.
 * 4) Add the sugar, and cook until you get a one-string syrup.
 * 5) Cool the syrup, then store in air-tight container.

Jigarthanda ice cream

 * 1) Boil the milk, stirring continuously until it is frothy. Collect the malai (thick cream) that forms.
 * 2) Beat the fresh cream, and stir it into the milk. Reduce the heat to medium-low.
 * 3) Stir in the ¼ cup sugar until completely dissolved.
 * 4) Add the milk solids, and mix well. Let cool slightly.
 * 5) Heat the 2 tbsp sugar in a heavy-bottomed saucepan over low heat until it melts and caramelizes.
 * 6) Quickly and carefully add the hot milk mixture. It will sizzle. If the caramel seizes, keep heating it and it will melt in slowly.
 * 7) Let cool, then pour into an airtight container and cover it with cling wrap. Freeze for 4–5 hours.
 * 8) Once it sets, beat it well using a whisk or a blender. Repeat 3–4 times for creamier ice cream.
 * 9) Freeze for 5–6 hours.

Jigarthanda milk

 * 1) Simmer the milk in a heavy-bottomed saucepan until it is thickened and reduced to half its volume. Collect the malai (thick cream) that forms, and reserve it.
 * 2) In another pan, gently heat the sugar until it melts and caramelizes.
 * 3) Stir the caramel into the milk. Mix it well until it is fully dissolved and the milk turns golden in color.
 * 4) Simmer the milk for 10 minutes.
 * 5) Let it cool and keep it in fridge.

Assembly

 * 1) Add 1–2 tbsp soaked almond gum and 1 tbsp sarsaparilla syrup to a tall glass.
 * 2) Add enough jigarthanda milk to fill the glass ¾ full.
 * 3) Add a scoop of the jigarthanda ice cream.
 * 4) Top with the collected malai, and serve immediately.

title: Cookbook:Jigarthanda Milk


text:
User:Arlo Barnes/sandbox

 * ../glossing
 * ../myrmecology
 * ../drinking water

title: User:Arlo Barnes/sandbox


text:
User:Arlo Barnes/myrmecology

Myrmecology is the study of ants.

 * /natural history — evolutionary origins and fortunes
 * /scientific history — who are the myrmecologists?
 * /the individual — anatomy, behaviour, and sensorium
 * /the caste — roles in the colony
 * /the colony — the superorganismal unit
 * /the ecology — life between colonies and regarding other organisms
 * /in the lab — care and keeping of ants
 * /taxonomy — how the diversity is [dis]organised
 * /what they teach us — stigmergy, logistics, and modelling

title: User:Arlo Barnes/myrmecology


text: Category:Pages transcluding nonexistent sections


text:
Circuit Idea/Expanding the Toolbox

In addition to methods already discussed:

 * Shattering
 * Merging
 * Periodic operation
 * Turning the harmful into useful
 * Dynamization

... there are more universal methods for solving inventive tasks.

Compensation
According to this idea, the unwanted quantity is suppressed by adding an "anti-quantity" with the same value to it. The method is widely applied in all fields of technology.

A. Compensating for gravitational attraction (the weight of objects)

Did you know that the elevator car you travel in every day is almost weightless? This is due to the so-called "counterweight" that compensates for the weight of the cabin. Thanks to this, electricity is saved and the use of a relatively low-power motor is possible (with full compensation, only frictional forces are overcome). Thanks to the counterweights, the rail barriers become light as a feather. Again, with their help, people from ancient times extracted water from their wells without much effort.

Where it is impossible to hang an anti-weight, it is created by other means. Examples of this are air balloons, airships, airplanes, helicopters, submarines, etc., which move in the respective environment thanks to an artificially created lifting force. "Anti-weight" can be created using magnetic forces. The so-called magnetic suspension reduces the friction in supports and rotating bodies (flywheels, turbine rotors, etc.) many times.

B. Compensation of mechanical oscillations.

Until recently, the fight against noise was carried out only by passive means - absorption of noise with a variety of porous materials. But here an active method was proposed - noise suppression with "anti-noise". For this purpose, loudspeakers are placed near the noise source, which emit noise of the same amplitude but with the opposite phase. The result is... silence.

C. Compensation of electrical quantities.

An example of this is the differential amplifier, which amplifies only the useful signal and suppresses the interference. Another example is the separation of the variable or constant component of a mixed signal.

D. The value of a quantity is measured by compensating it with a reference quantity.

This is how all types of weights work. Extremely simple electrical measuring devices can also be constructed in this way. How, for example, would we measure the voltage in an electrical circuit without an accurate meter? Of course, by the compensation method. A zero indicator is zeroed with a potentiometer. The voltage value is read on the potentiometer scale. If the zero indicator is implemented with LEDs, the entire device can be mounted in a pen housing.

Single use
Our century can rightly be called the century of disposable items. They quickly entered the household and replaced the solid objects of the recent past. Such are, for example, the plastic cups in which we drink coffee, cola, tea (and irresponsibly throw away afterwards); the plastic packaging for all food products, medicines and miscellaneous items; disposable pens, gas lighters, deodorants, paints, varnishes and others in aerosol packaging. New disposable items are constantly appearing, some of which seem downright absurd - disposable toothbrushes, thermometers, trash cans, etc. Perhaps electronic wristwatches, calculators and pocket radios will also become disposable when their cost becomes commensurate with that of the batteries that power them. Of course, there are also more serious applications of the method - for example, disposable weather probes or rockets.

"Matryoshka" method
The popular Russian matryoshka dolls, which are placed inside each other, successfully illustrate the essence of this method. The idea is very old - even in ancient times, Russian craftsmen made wooden vessels that were placed inside each other. And even now, tourists widely use matryoshka dishes (cups, pots, etc.). The benefit is obvious - space is saved. Telescopic antennas for radio receivers are also a kind of "Matryoshka". The weather "matryoshka balloons" proposed by the Soviet inventor Ermakov are several multi-colored alloons, nested inside each other. By bursting successively at different heights, the color of the balloon changes (handy for monitoring air flows).

And here is an application in electronics - an LED indicator of the "glowing dot" type. Its operation is based on the fact that the IV curves of LEDs SD1-SD10 are located one inside the other, similar to Russian "Matryoshkas". This was achieved using silicon diodes D1-D9.

Self-service
The object serves itself by performing auxiliary operations. A typical example of this is a car engine. In addition to its main task - driving the car, it also performs operations necessary for its proper functioning - charging the battery, driving the fuel, oil and water pumps.

An interesting illustration of the method is the self-propelled cart set in motion by the load. Under the action of its weight, the platform of the cart descends, and the rack connected to it turns the wheels. After unloading, springs return the platform to its initial position. The self-service method has been perfected by the inventors of perpetual motion machines.A generator and electric motor connected electrically and mechanically are completely self-sustaining and should run forever. That this is impossible is known to each of us today.

Universality
The object performs several functions, which is why there is no need for other objects. The concrete mixer-car simultaneously mixes the concrete and transports it. Water fishing vessels are intended for fishing, processing and transport of fish. A significant simplification of the devices is obtained if the reversible properties of some objects (electric motors, loudspeakers, piezo elements, etc.) are used. In some radio telephones, for example, an electrodynamic speaker is used, which also performs the function of a microphone. The radar antenna and echo sounder piezo element can receive and emit signals.

"Upside" ("turn on its head")
Instead of the action dictated by the task conditions, the opposite action is performed. How were the reversible properties of piezo elements discovered, for example? By the "upside down" method. Let's assume that initially only the straight piezo effect was known - the occurrence of an electric charge during mechanical deformation of the piezo crystal. The question "What will happen if we do the opposite?" has led to the discovery of the reverse piezo effect - mechanical deformation of the piezo crystal under the action of an electric field. Until a few years ago, pocket electric flashlights had an invariable design - a straight placement of the lamp in the reflector. But now there are also flashlights with a "reverse" arrangement of the lamp, which are thinner.

Inventor's "toolkit" contains more than 100 methods for solving inventive tasks. Naturally, we do not have the opportunity to consider all of them, so we limited ourselves to the most universal of them. Each inventor can create his own methods. The only condition is that they are sufficiently universal (that is, the method discovered in solving a certain inventive task can be used to solve tasks in completely other fields of technology). How are methods used to solve inventive tasks in practice? In the simplest case, they apply directly - after specifying the conditions of the task, we "open the toolbox" and look for the most suitable one. But there are more rational ways to use the methods. One of them is called algorithm for solving inventive tasks (ARIZ) and was developed by the Soviet inventor Henrich Altshuler. ARIZ divides the creative process into three stages: analytical, operational and synthetic. Each of them contains separate steps, the sequential implementation of which brings the inventor closer to the technical solution of the task. Detailed sacred information about ARIZ can be obtained from the attached literature.

title: Circuit Idea/Expanding the Toolbox


text:
Fractals/Esher like tilings

=name=
 * name is misleading because there is no tiling here ( no tiles)
 * nam comes from the book The Science of fractal images by Heinz-Otto Peitgen, Dietmar Saupe, Springer (page 187 )

=algorithm= Escher like tilings is a modification of the level set method ( LSM/J). Here Level sets of escape time are different because targest set is different. Here target set is a scalled filled-in Julia set.

For more description see
 * Fractint : escher_julia
 * page 187 from The Science of fractal images by Heinz-Otto Peitgen, Dietmar Saupe, Springer

=Images=

=References=

title: Fractals/Esher like tilings


text:
Circuit Idea/Crystallization of the Idea

The first signs of a nascent new idea are usually too vague. At this point, you want to pounce on the idea, to fully realize it, subjecting it to rigorous logical thinking. The result of this is deplorable - you deprive the idea of the opportunity to grow in a random and original way, you cut it off from its natural environment.

What should we do in order not to "kill" the new idea in its infancy?

First, let's try to keep it in our head for a while longer. Only when we feel that it has matured enough can we transfer it from the mental screen to a piece of paper or express it in words. But this should also be done carefully. Outline the idea (verbally or in writing) as broadly as possible. Pencil, soft eraser and paper - these are the most suitable tools for the purpose. Remember well: it is sketched casually, not drawn with a ruler and compass, so that you will not regret the effort when you have to erase repeatedly. Now it is important to answer the question: is the device operational? Only when we are satisfied that the answer is positive can we move on to detailed design development involving technical drawing, calculations, etc.

At this point, you are dying to experiment with the new device. Attention! There is also danger here. Prematurely dressing the idea in a construction freezes it in a state that is perhaps only an intermediate stage in its development. Therefore, it is desirable to initially make a very elementary model (mock-up) with the means at hand. If the invention is a mechanical construction, soft and plastic materials are suitable (soft wire, tinol, plasticine, styrofoam, and also details from children's constructors), and the electronic circuit is good to "stick" quickly (even carelessly) on a breadboard. Such models are quickly and easily modified, without regretting any of the numerous options. If, instead of plasticine, you had prepared the mechanical model by a milling machine, and the electronic one on a beautiful printed circuit board from foiled textolite, you would hardly have been able to afford further changes to these finished and perfect at first glance constructions.

After the idea has fully matured and you are deeply convinced of its rightness, you can share it with someone. But with whom? The moment of sharing is interesting from a psychological point of view in that the one who shares his own idea is at a disadvantage compared to his interlocutor. (In a similar situation is a young poet who is about to read his poems for the first time in front of someone he knows.) And if he turns out to be a well-educated but tactless specialist, as happens most often, you are in for a derisive attitude, taunts or at best a condescending pat on the back. After all, this is completely natural. You have dared to enter his domain, nay, you claim to have invented a more perfect device than any known to him. Therefore, run away from such "critics" of new ideas! Otherwise, you risk getting an ice shower that will cool your creative enthusiasm for a long time.

In this sense, it is desirable to share your idea with non-specialists in the given field. They will not subject it to destructive criticism because they do not have excessive self-confidence. At the expense of this, however, they can express interesting thoughts and considerations for its further development and application. Even just saying the idea, asking the right question can enrich it with new interesting thoughts.

At this stage, you may experience another disappointment - the possibility that your solution was previously reached by other inventors, ie. as some would say ironically, you have reinvented the bicycle. There is nothing wrong with this. The fact that the invention has already been made does not diminish your credit as an inventor, if, of course, you did not know about it and independently came to the same decision. What is more, you can even be happy that your idea is useful and applicable. The effort spent was not in vain, and sooner or later you will make a real invention.


text:
User:Garfieldcat1978/Report.js

// /* To use, simply add "mw.loader.load('//en.wikibooks.org/w/index.php?title=User:L10nM4st3r/ReportUser.js&action=raw&ctype=text/javascript');" to you /common.js subpage. After doing that, go to RC, look for a user making really bad edits, and go to their userpage, talkpage, or contributions page. Press the "report" tab and give a reason to report them. Then they will automatically be reported to the admins. On TODO list: * Use custom UI, rather than being lazy and using a very limited prompt command. * Allow using preset reasons, maybe. Would be quite difficult though. * Check if user is already blocked.

// Will be used to make sure the user uses the newest version. Currently no idea how to implement this though. const build=1; const version="0.0.4";

/////////// Settings the user can change ////// var force_enabled_for_admins=false;// If true, even admins can use the script. var can_report_self=false;// If true, the user can report themselves. Useful for testing the script.

function success{ if(same){ same=false; mw.notify("User already reported",{type:'error'}); }	else mw.notify("Successfuly reported user!"); } function failed{ if(same){ same=false; mw.notify("User already reported",{type:'error'}); }	else mw.notify("Unable to report user. Perhaps you don't have permission to edit your local vandalism reporting page?",{type:'error'}); } // Used in getting the correct error message. Do not modify deafult value. var same=false;

$.when($.ready,mw.loader.using(['mediawiki.util','mediawiki.api'])).then( function{

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// User must be autoconfirmed to use this script in the first place. && mw.config.get('wgUserGroups').includes('autoconfirmed')){	var node=mw.util.addPortletLink('p-cactions','','Report','utreportuser',"Report this user to the local admins.");	$(node).on('click',function(e){ var user=mw.config.get('wgRelevantUserName'); var reason=prompt("Give a reason for reporting "+user+".\n\nExamples: spam, vandalism, blanking pages, LTA, long-term abuse\n\nLeave blank to cancel."); // There MUST be a reason filled out for the edit to take place if(reason) { var ad=" (using ReportUser "+version+")"; var summary="Reporting user "+user+" (talk · contribs)"; var tag=''; var full_reason=reason+' '+tag; // Report user, depending on the wiki

///////// en wikibooks ///////// if(mw.config.get('wgDBname')=='enwikibooks') new mw.Api.edit('Wikibooks:Reading_room/Administrative_Assistance',function(revision){					ad=" (using ReportUser "+version+")";					if (revision.content.includes('')){same=true;return{text:revision.content}}					return {						text: revision.content+"\n\n==Please block "+user+' (talk · contribs)==\nReason: '+full_reason+' ~',						summary: summary+ad,					};				}).then(function{success},function{failed});

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}		else // No reason given. Aborted the report mw.notify('You must give a reason to request to have this user blocked.',{type:'error'}); e.preventDefault; }); }}); //

title: User:Garfieldcat1978/Report.js


text:
User talk:KatTeague

Garfieldcat1978 (discuss • contribs) 19:40, 22 February 2023 (UTC)

title: User talk:KatTeague


text:
User talk:FCLMari029

Garfieldcat1978 (discuss • contribs) 19:41, 22 February 2023 (UTC)

title: User talk:FCLMari029


text:
User talk:Dorota2023

Garfieldcat1978 (discuss • contribs) 19:41, 22 February 2023 (UTC)

title: User talk:Dorota2023


text:
User talk:GetWellDr.

Garfieldcat1978 (discuss • contribs) 19:46, 22 February 2023 (UTC)

title: User talk:GetWellDr.


text:
User talk:NightWolf1223

Garfieldcat1978 (discuss • contribs) 19:48, 22 February 2023 (UTC)

title: User talk:NightWolf1223


text:
The Legend of Zelda: Breath of the Wild/Divine Beasts

Order
The divine beasts are usually completed this order.
 * 1) Divine Beast Vah Ruta
 * 2) Divine Beast Vah Rudania
 * 3) Divine Beast Vah Medoh
 * 4) Divine Beast Vah Naboris

That said, the divine beasts can be completed in any order the player wishes.

Vah Ruta
The divine beast of the Zora.

Specilized arrows are required to board Vah Ruta.

The boss of Vah Ruta is Waterblight Ganon.

Completion of this divine beast grants the player an automatic revival when they run out of health. This ability can be used just once before it must recharge.

Vah Rudania
The divine beast of the Goron.

The interior of Vah Rudania is initially unlit, unlike most of the divine beasts.

The boss of Vah Rudania is Fireblight Ganon.

Completion of this divine beast grants the player the ability to create a near perfect shield while guarding, allowing for most attacks to automatically be ignored. This ability can be used just a few times before it must recharge.

Vah Medoh
The divine beast of the Rito.

Familiarity with slow motion bow shooting helps with boarding Vah Medoh.

The boss of Vah Medoh is Windblight Ganon.

Completion of this divine beast grants the player the ability to create and then paraglide on an updraft at will, greatly expanding mobility options. This ability can only be used a few times before it must recharge.

Vah Naboris
The divine beast of the Gerudo.

Specialized arrows are required to board Vah Naboris. Familiarity with Sand Seal riding makes the boarding easier.

The boss of Vah Naboris is Thunderblight Ganon.

Completion of this divine beast allows the player to unleash a electrical attack when they pause to "charge" their weapon for an otherwise normal strong attack. This ability can only be used a few times before recharging is required.


text: Category:Book:The Legend of Zelda: Breath of the Wild


text:
The Legend of Zelda: Breath of the Wild/Weapons

Woodcutter
A woodcutter's tool of choice felling trees. It's formidable weight and uneven balancing make it a slow, ineffcient weapon.

Rusty
This once-fearsome sword has seen better days. It can do some damage in the right hands, but, also breaks quickly.

Traveler
A very common sword often keep by travelers to fall off small beasts. It's fairly durable, but, a bit unreliable against monsters.

Soldier
A bow designed for armed conflict. Inflicents more damage than a civilan bow, but, it will still break if it touches fire.

Traveler
A small bow used by travelers for protection. It doesn't do a of damage, but, it can be used to attack foes frrom a distance.

Arrow
x5 - A bundle of five common arrows. The shafts of these arrows we're from the wood of a sturdy tree.


text:
The Legend of Zelda: Breath of the Wild/Shrines

Shrines serve as miniature dungeons. Completion of the shrine awards the player a Spirit Orb, alongside other potential benefits.

Main Quest
Follow the Sheikah Slate

Shrine Quests
Occasionally shrines will require a quest before being allowed to enter.

Puzzles
Many shrines revolve around using game mechanics to reach a goal. Sometimes you need to use Cryonis to build blocks of ice while other times may necessitate the use of Magnesis to pick up metal items. Fire may be needed to destroy vines and bombs could be used to blow holes in bombable blocks.

Gyro Shrines
Shrines revolving around the use of gyroscopic manipulation to solve a puzzle.

Tests of Strength
These combat oriented shrines test the player in combat, with victory resulting in completion of the shrine.

Blessing
Blessing shrines immediately award the player with a spirit orb. That is not to say blessing shrines are a freebie for the player, these shrines are typically protected by some sort of puzzle or quest in the overworld.

Ballad of the Champions Shrines
These shrines have special rules that make their completion more difficult then many standard shrines.


text:
The Legend of Zelda: Breath of the Wild/Materials

Materials are a key gameplay mechanic and play a role in a variety of activites. Materials are central to cooking, potion making, equipment enchanting, and a number of quests.


text:
User talk:2601:204:4100:AC60:5187:DAE4:E34C:BE44

--Xania   talk 01:06, 23 February 2023 (UTC)


text:
User talk:2600:1700:3D70:AB90:DC72:96F4:9465:D099

--Xania   talk 01:37, 23 February 2023 (UTC)


text:
User:SSastry (WMF)/Sandbox

a b1 b2 b3

a-a a-b1 a-b2

A-a A-b1 A-b2

r-a r-b1 r-b2

R-a R-b1 R-b2

d-a d-b1 d-b2

g-a g-b1 g-b2

X-a X-b1 X-b2

title: User:SSastry (WMF)/Sandbox


title: User:Aryakin2020


text:
User:Alheit

...

title: User:Alheit


text:
User talk:DeirgeDel

'''This is the talk page for DeirgeDel, the successor sccount to the abandoened Djm-leighpark account, and any matters relating to Djm-leighpark may be brought here. Please add new discussions to the bottom of the page. Thankyou.'''

title: User talk:DeirgeDel


text:
Fractals/Mathematics/periodic points of complex quadratic map

=Periodic points of complex quadratic map= This article describes periodic points of some complex quadratic maps. A map is a formula for computing a value of a variable based on its own previous value or values; a quadratic map is one that involves the previous value raised to the powers one and two; and a complex map is one in which the variable and the parameters are complex numbers. A periodic point of a map is a value of the variable that occurs repeatedly after intervals of a fixed length.

These periodic points play a role in the theories of Fatou and Julia sets.

Definitions
Let

 * $$f_c(z) = z^2+c\,$$

be the complex quadric mapping, where $$z$$ and $$c$$ are complex numbers.

Notationally, $$f^{(k)} _c (z)$$ is the $$k$$-fold composition of $$f_c$$ with itself (not to be confused with the $$k$$th derivative of $$f_c$$)—that is, the value after the k-th iteration of the function $$f _c.$$ Thus

 * $$f^{(k)} _c (z) = f_c(f^{(k-1)} _c (z)).$$

Periodic points of a complex quadratic mapping of period $$p$$ are points $$z$$ of the dynamical plane such that

 * $$f^{(p)} _c (z) = z,$$

where $$p$$ is the smallest positive integer for which the equation holds at that z.

We can introduce a new function:

 * $$F_p(z,f) = f^{(p)} _c (z) - z,$$

so periodic points are zeros of function $$F_p(z,f)$$: points z satisfying

 * $$F_p(z,f) = 0,$$

which is a polynomial of degree $$2^p.$$

Number of periodic points
The degree of the polynomial $$F_p(z,f)$$ describing periodic points is $$d = 2^p$$ so it has exactly $$d = 2^p$$ complex roots (= periodic points), counted with multiplicity.

Stability of periodic points (orbit) - multiplier

The multiplier (or eigenvalue, derivative) $$m(f^p,z_0)=\lambda$$ of a rational map $$f$$ iterated $$p$$ times at cyclic point $$z_0$$ is defined as:

 * $$m(f^p,z_0) = \lambda = \begin{cases}

f^{p \prime}(z_0), &\mbox{if }z_0 \ne \infty \\ \frac{1}{f^{p \prime} (z_0)}, & \mbox{if }z_0 = \infty \end{cases}$$

where $$f^{p\prime} (z_0)$$ is the first derivative of $$f^p$$ with respect to $$z$$ at $$z_0$$.

Because the multiplier is the same at all periodic points on a given orbit, it is called a multiplier of the periodic orbit.

The multiplier is:
 * a complex number;
 * invariant under conjugation of any rational map at its fixed point;
 * used to check stability of periodic (also fixed) points with stability index $$abs(\lambda). \,$$

A periodic point is
 * attracting when $$abs(\lambda) < 1;$$
 * super-attracting when $$abs(\lambda) = 0;$$
 * attracting but not super-attracting when $$0 < abs(\lambda) < 1;$$
 * indifferent when $$abs(\lambda) = 1;$$
 * rationally indifferent or parabolic if $$\lambda$$ is a root of unity;
 * irrationally indifferent if $$abs(\lambda)=1$$ but multiplier is not a root of unity;
 * repelling when $$abs(\lambda) > 1.$$

Periodic points
 * that are attracting are always in the Fatou set;
 * that are repelling are in the Julia set;
 * that are indifferent fixed points may be in one or the other. A parabolic periodic point is in the Julia set.

Finding periodic points
solve these equations using numerical methods for solving polynomials - and even something simple such as Newton's method is going to converge a lot faster than finding the cycles just by iterating a single point (as is how bifurcations diagrams are usually made) under fc itself. Milo Brandt

Methods:
 * simple iterating and checking convergence
 * numerical methods
 * symbolic computations, algebraic
 * numerical methods for finding roots of polynomial equations

Finite fixed points
Let us begin by finding all finite points left unchanged by one application of $$f$$. These are the points that satisfy $$f_c(z)=z$$. That is, we wish to solve

 * $$z^2+c=z,\,$$

which can be rewritten as

 * $$\ z^2-z+c=0.$$

Since this is an ordinary quadratic equation in one unknown, we can apply the standard quadratic solution formula:

 * $$\alpha_1 = \frac{1-\sqrt{1-4c}}{2}$$ and $$\alpha_2 = \frac{1+\sqrt{1-4c}}{2}.$$

So for $$c \in \mathbb{C} \setminus \{1/4\}$$ we have two finite fixed points $$\alpha_1$$ and $$\alpha_2$$.

Since
 * $$\alpha_1 = \frac{1}{2}-m$$ and $$\alpha_2 = \frac{1}{2}+m$$ where $$m = \frac{\sqrt{1-4c}}{2},$$

we have $$\alpha_1 + \alpha_2 = 1$$.

Thus fixed points are symmetrical about $$z = 1/2$$.

Complex dynamics

Here different notation is commonly used:

 * $$\alpha_c = \frac{1-\sqrt{1-4c}}{2}$$ with multiplier $$\lambda_{\alpha_c} = 1-\sqrt{1-4c}$$

and

 * $$\beta_c = \frac{1+\sqrt{1-4c}}{2}$$ with multiplier $$\lambda_{\beta_c} = 1+\sqrt{1-4c}.$$

Again we have

 * $$\alpha_c + \beta_c = 1 .$$

Distance between fixed points:

 * $$\frac{1- \Delta}{2} < \frac{1}{2} < \frac{1 + \Delta}{2}$$

is delta $$\Delta$$

where

 * $$\Delta = \sqrt{1 - 4c}$$ so

 * for $$c = \frac{1}{4}$$ distance is equal to zero:  $$\Delta(\frac{1}{4}) = \sqrt{0} = 0 $$ =the points coincide ( parabolic case)
 * for $$c = 0$$ distance is equal to 1:  $$\Delta(1) = \sqrt{1} = 1 $$ = the superattracting case ( alfa is a center and beta in on the unit circle)

Since the derivative with respect to z is

 * $$P_c'(z) = \frac{d}{dz}P_c(z) = 2z ,$$

we have

 * $$P_c'(\alpha_c) + P_c'(\beta_c)= 2 \alpha_c + 2 \beta_c = 2 (\alpha_c + \beta_c) = 2 .$$

This implies that $$P_c$$ can have at most one attractive fixed point.

These points are distinguished by the facts that:
 * $$\beta_c$$ is:
 * the landing point of the external ray for angle=0 for $$c \in M \setminus \left\{ 1/4 \right\}$$
 * the most repelling fixed point of the Julia set
 * the one on the right (whenever fixed point are not symmetrical around the real axis), it is the extreme right point for connected Julia sets (except for cauliflower).
 * $$\alpha_c$$ is:
 * the landing point of several rays
 * attracting when $$c$$ is in the main cardioid of the Mandelbrot set, in which case it is in the interior of a filled-in Julia set, and therefore belongs to the Fatou set (strictly to the basin of attraction of finite fixed point)
 * parabolic at the root point of the limb of the Mandelbrot set
 * repelling for other values of $$c$$

Special cases

An important case of the quadratic mapping is $$c=0$$. In this case, we get $$\alpha_1 = 0$$ and $$\alpha_2=1$$. In this case, 0 is a superattractive fixed point, and 1 belongs to the Julia set.

Only one fixed point

We have $$\alpha_1=\alpha_2$$ exactly when $$1-4c=0.$$ This equation has one solution, $$c=1/4,$$ in which case $$\alpha_1=\alpha_2=1/2$$. In fact $$c=1/4$$ is the largest positive, purely real value for which a finite attractor exists.

Infinite fixed point
We can extend the complex plane $$\mathbb{C}$$ to the Riemann sphere (extended complex plane) $$\mathbb{\hat{C}}$$ by adding infinity:

 * $$\mathbb{\hat{C}} = \mathbb{C} \cup \{ \infty \}$$

and extend $$f_c$$ such that $$f_c(\infty)=\infty.$$

Then infinity is:
 * superattracting
 * a fixed point of $$f_c$$: $$f_c(\infty)=\infty=f^{-1}_c(\infty).$$

Period-2 cycles
Period-2 cycles are two distinct points $$\beta_1$$ and $$\beta_2$$ such that $$f_c(\beta_1) = \beta_2$$ and $$f_c(\beta_2) = \beta_1$$, and hence

 * $$f_c(f_c(\beta_n)) = \beta_n$$

for $$n \in \{1, 2\}$$:

 * $$f_c(f_c(z)) = (z^2+c)^2+c = z^4 + 2cz^2 + c^2 + c.$$

Equating this to z, we obtain

 * $$z^4 + 2cz^2 - z + c^2 + c = 0.$$

This equation is a polynomial of degree 4, and so has four (possibly non-distinct) solutions. However, we already know two of the solutions. They are $$\alpha_1$$ and $$\alpha_2$$, computed above, since if these points are left unchanged by one application of $$f$$, then clearly they will be unchanged by more than one application of $$f$$.

Our 4th-order polynomial can therefore be factored in 2 ways:

First method of factorization

 * $$(z-\alpha_1)(z-\alpha_2)(z-\beta_1)(z-\beta_2) = 0.\,$$

This expands directly as $$x^4 - Ax^3 + Bx^2 - Cx + D = 0$$ (note the alternating signs), where

 * $$D = \alpha_1 \alpha_2 \beta_1 \beta_2, \,$$

 * $$C = \alpha_1 \alpha_2 \beta_1 + \alpha_1 \alpha_2 \beta_2 + \alpha_1 \beta_1 \beta_2 + \alpha_2 \beta_1 \beta_2, \,$$

 * $$B = \alpha_1 \alpha_2 + \alpha_1 \beta_1 + \alpha_1 \beta_2 + \alpha_2 \beta_1 + \alpha_2 \beta_2 + \beta_1 \beta_2, \,$$

 * $$A = \alpha_1 + \alpha_2 + \beta_1 + \beta_2.\,$$

We already have two solutions, and only need the other two. Hence the problem is equivalent to solving a quadratic polynomial. In particular, note that

 * $$\alpha_1 + \alpha_2 = \frac{1-\sqrt{1-4c}}{2} + \frac{1+\sqrt{1-4c}}{2} = \frac{1+1}{2} = 1$$

and

 * $$\alpha_1 \alpha_2 = \frac{(1-\sqrt{1-4c})(1+\sqrt{1-4c})}{4} = \frac{1^2 - (\sqrt{1-4c})^2}{4}= \frac{1 - 1 + 4c}{4} = \frac{4c}{4} = c.$$

Adding these to the above, we get $$D = c \beta_1 \beta_2$$ and $$A = 1 + \beta_1 + \beta_2$$. Matching these against the coefficients from expanding $$f$$, we get

 * $$D = c \beta_1 \beta_2 = c^2 + c$$ and $$A = 1 + \beta_1 + \beta_2 = 0.$$

From this, we easily get

 * $$\beta_1 \beta_2 = c + 1$$ and $$\beta_1 + \beta_2 = -1$$.

From here, we construct a quadratic equation with $$A' = 1, B = 1, C = c+1$$ and apply the standard solution formula to get

 * $$\beta_1 = \frac{-1 - \sqrt{-3 -4c}}{2}$$ and $$\beta_2 = \frac{-1 + \sqrt{-3 -4c}}{2}.$$

Closer examination shows that:

 * $$f_c(\beta_1) = \beta_2$$ and $$f_c(\beta_2) = \beta_1,$$

meaning these two points are the two points on a single period-2 cycle.

Second method of factorization
We can factor the quartic by using polynomial long division to divide out the factors $$(z-\alpha_1)$$ and $$(z-\alpha_2), $$ which account for the two fixed points $$\alpha_1$$ and $$\alpha_2$$ (whose values were given earlier and which still remain at the fixed point after two iterations):

 * $$(z^2+c)^2 + c -z = (z^2 + c - z)(z^2 + z + c +1 ). \,$$

The roots of the first factor are the two fixed points. They are repelling outside the main cardioid.

The second factor has the two roots

 * $$\frac{-1 \pm \sqrt{-3 -4c}}{2}. \,$$

These two roots, which are the same as those found by the first method, form the period-2 orbit.

Special cases
Again, let us look at $$c=0$$. Then

 * $$\beta_1 = \frac{-1 - i\sqrt{3}}{2}$$ and $$\beta_2 = \frac{-1 + i\sqrt{3}}{2},$$

both of which are complex numbers. We have $$| \beta_1 | = | \beta_2 | = 1$$. Thus, both these points are "hiding" in the Julia set. Another special case is $$c=-1$$, which gives $$\beta_1 = 0$$ and $$\beta_2 = -1$$. This gives the well-known superattractive cycle found in the largest period-2 lobe of the quadratic Mandelbrot set.

Cycles for period greater than 2
The degree of the equation $$f^{(n)}(z)=z$$ is 2n; thus for example, to find the points on a 3-cycle we would need to solve an equation of degree 8. After factoring out the factors giving the two fixed points, we would have a sixth degree equation.

There is no general solution in radicals to polynomial equations of degree five or higher, so the points on a cycle of period greater than 2 must in general be computed using numerical methods. However, in the specific case of period 4 the cyclical points have lengthy expressions in radicals.

In the case c = –2, trigonometric solutions exist for the periodic points of all periods. The case $$z_{n+1}=z_n^2-2$$ is equivalent to the logistic map case r = 4: $$x_{n+1}=4x_n(1-x_n).$$ Here the equivalence is given by $$z=2-4x.$$ One of the k-cycles of the logistic variable x (all of which cycles are repelling) is

 * $$\sin^2\left(\frac{2\pi}{2^k-1}\right), \, \sin^2\left(2\cdot\frac{2\pi}{2^k-1}\right), \, \sin^2\left(2^2\cdot\frac{2\pi}{2^k-1}\right), \, \sin^2\left(2^3\cdot\frac{2\pi}{2^k-1}\right), \dots, \sin^2\left(2^{k-1}\frac{2\pi}{2^k-1}\right).$$

Method by Claude Heiland-Allen
What I do to create an periodic components of Mandelbrot set, for $$f_c(z) = z^2 + c$$:
 * start iteration from $$z_0 := 0$$, with $$m := \infty$$
 * for each $$n = 1, 2, 3, ...$$ in order
 * calculate $$z_n := f_c(z_{n-1})$$
 * if $$|z_n| < m$$
 * set $$m := |z_n|$$
 * use Newton's method to solve $$w = f_c^{\circ n}(w)$$ with initial guess $$w^{(0)} := z_n$$ (this may fail to converge, in which case continue with the next $$n$$), the steps are $$w^{(i+1)} := w^{(i)} - \frac{f_c^{\circ n}(w^{(i)}) - w^{(i)}}{{f_c^{\circ n}}'(w^{(i)}) - 1}$$
 * calculate the derivative of the cycle $$\lambda := {f_c^{\circ n}}'(w)$$
 * if $$|\lambda| < 1$$, then the cycle is attractive and $$c$$ is within a hyperbolic component of period $$n$$, stop (success).

Where:
 * $$\lambda$$ may used as "interior coordinates" within the hyperbolic component.
 * $$w$$ and $$n$$ can be used for interior distance estimation.

The point of using Newton's method is to accelerate the computation of $$w$$, a point in the limit cycle attractor. Computing $$w$$ just by iterating $$f_c$$ could take many 1000s of iterations, especially when $$\lambda$$ is close to $$1$$.

I have no complete proof of correctness (but this doesn't mean I think it is incorrect; the images seem plausible). It relies on the "atom domains" surrounding each hyperbolic component of a given period.

It also relies on the cycle reached by Newton's method being the same cycle as the limit cycle approached by iteration: this is true for the quadratic Mandelbrot set because there is only one finite critical point, $$0$$ ($$\infty$$ is a fixed point) and each attracting or parabolic cycle has a critical point in its immediate basin (see ), which means there can be at most one attracting or parabolic cycle.

For an implementation in C99 you can see my blog post at

Speed up
Cardioid / bulb checking:


text:
User talk:James0786

I saw your note about how to type sigma in the Calculus book, and I just wanted to say Welcome!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally.

Links to howtotypesymbols.com
Omphalographer (discuss • contribs) 19:08, 27 March 2023 (UTC)

 * Thank you for your message. This page is about phi symbol and I have added a link about how to type phi symbol. I thought this is relevant because if someone is looking for it, maybe it will be beneficial for them. I'm sorry. 154.192.18.23 (discuss) 19:10, 27 March 2023 (UTC)

title: User talk:James0786


text:
User talk:Bykim2012

Welcome, Bykim2012!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally.

--Xania   talk 02:32, 24 February 2023 (UTC)

title: User talk:Bykim2012


text:
User:Yibanathi Ngcupe

I am an aspiring writer and musician, hoping to gain a competitive advantage in industry !

title: User:Yibanathi Ngcupe


text:
Talk:Physics Using Geometric Algebra

Geometric Algebra Name Use Confusion
There is confusion being caused by different people using "Geometric Algebra" to refer to different Clifford Algebra formalisms.Could a concensus be reached on how to distinguish among the different formalisms?

1. Applied Geometric Algebra, László Tisza 2. Algebra of Physical Space, W.E. Baylis 3. Geometric Algebra, David Hestenes Bluegiant69202 (discuss • contribs) 01:40, 25 February 2023 (UTC)

title: Talk:Physics Using Geometric Algebra


text:
Talk:Physics Using Geometric Algebra/Relativistic Classical Mechanics/References

Mention of different formalisms
Both links on this page are dead and alternative references to the work of William E. Baylis should be added. I would also like to discuss adding references to the Primer on Geometric Algebra for High School Students, the GA R&D website and the Cambridge University Geometric Algebra Website.

Some sources of other information
The web site of William E. Baylis has some extended information on the subset of the covariant formalism of Clifford’s geometric algebra of physical space (APS). Note should be made of differences in terminology and notation from the Geometric Algebra formalism developed by David Hestenes et al.

In particular, Relativity in Introductory Physics explains in more detail some of the notation used in this wikibook.

Baylis, William E.. “Relativity in introductory physics.” Canadian Journal of Physics 82 (2004): 853-873. arXiv:physics/0406158v3

Relativity in introductory physics - arxiv.org. (n.d.). Retrieved February 24, 2023, from https://arxiv.org/pdf/physics/0406158.pdf

Baylis, William E. Clifford (Geometric) Algebras with Applications to Physics, Mathematics, and Engineering. Birkhäuser, 1996.

Baylis, W. E. "Special relativity with 2× 2 matrices." American Journal of Physics 48.11 (1980): 918-925.

Sources using different terminology and a different notation system:

Doran, Chris, and A. N. Lasenby. Geometric Algebra for Physicists. Cambridge University Press, 2013

Hestenes, David. New Foundations for Classical Mechanics, 2nd edn., Kluwer Academic Publisher, 2003

Primer on Geometric Algebra for introductory mathematics and physics, Special Relativity with Geometric Algebra, Defining Spacetime http://geocalc.clas.asu.edu/GA_Primer/GA_Primer/special-relativity-with/defining-spacetime/index.html

“Geometric Algebra Resources.” Geometric Algebra, http://geometry.mrao.cam.ac.uk/

“Teaching Resources.” Geometric Algebra, http://geometry.mrao.cam.ac.uk/home/teaching-resources/

Applications of Geometric Algebra I, Physical Applications of Geometric Algebra: Part II, Relativistic Physics by Chris Doran and Anthony Lasenby - University of Cambridge. http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/01ApplicationsI.pdf

Geometric Calculus Research & Development, SpaceTime Calculus, https://geocalc.clas.asu.edu/html/STC.html.

Hestenes, David. SpaceTime Calculus, http://geocalc.clas.asu.edu/pdf/SpaceTimeCalc.pdf

Some sources of other information
The web site of William E. Baylis has some extended information on the subset of the covariant formalism of Clifford’s geometric algebra of physical space (APS). Note should be made of differences in terminology and notation from the Geometric Algebra formalism developed by David Hestenes et al.

In particular, Relativity in Introductory Physics explains in more detail some of the notation used in this wikibook.

Baylis, William E.. “Relativity in introductory physics.” Canadian Journal of Physics 82 (2004): 853-873. arXiv:physics/0406158v3

Relativity in introductory physics - arxiv.org. (n.d.). Retrieved February 24, 2023, from https://arxiv.org/pdf/physics/0406158.pdf

Baylis, William E. Clifford (Geometric) Algebras with Applications to Physics, Mathematics, and Engineering. Birkhäuser, 1996.

Baylis, W. E. "Special relativity with 2× 2 matrices." American Journal of Physics 48.11 (1980): 918-925.

Sources using different terminology and a different notation system:

Doran, Chris, and A. N. Lasenby. Geometric Algebra for Physicists. Cambridge University Press, 2013

Hestenes, David. New Foundations for Classical Mechanics, 2nd edn., Kluwer Academic Publisher, 2003

Primer on Geometric Algebra for introductory mathematics and physics, Special Relativity with Geometric Algebra, Defining Spacetime http://geocalc.clas.asu.edu/GA_Primer/GA_Primer/special-relativity-with/defining-spacetime/index.html

“Geometric Algebra Resources.” Geometric Algebra, http://geometry.mrao.cam.ac.uk/

“Teaching Resources.” Geometric Algebra, http://geometry.mrao.cam.ac.uk/home/teaching-resources/

Applications of Geometric Algebra I, Physical Applications of Geometric Algebra: Part II, Relativistic Physics by Chris Doran and Anthony Lasenby - University of Cambridge. http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/01ApplicationsI.pdf

Geometric Calculus Research & Development, SpaceTime Calculus, https://geocalc.clas.asu.edu/html/STC.html.

Hestenes, David. SpaceTime Calculus, http://geocalc.clas.asu.edu/pdf/SpaceTimeCalc.pdf Bluegiant69202 (discuss • contribs) 01:55, 25 February 2023 (UTC)


text: Talk:Chronicles of Narnia/Introduction/Intermediate


text:
User talk:6 kayla jean 6

Garfieldcat1978 (discuss • contribs) 19:33, 25 February 2023 (UTC)

title: User talk:6 kayla jean 6


text:
User:Garfieldcat1978/BJADON

If you're looking for the pages that were on Wikibooks Jokebook, please see lollerpedia.

Bad Jokes and Other Deleted Nonsense

I can't believe Wikipedia had the nerve to copy this idea from us. ;-)

From Grand Theft Auto: San Andreas/Missions/Home Coming
Hey this is K.C. from CV gimme an IV of straight coffee and some greens to keep me from goin' crazy, pickin' up this shit all day man my backs 'bout to break me. my friends all think I'm whack when I tell them I'm 'bout to slang some bags filled with this kid's crap. these hippies all want to hit me up for some acid as soon as I try to pass this plastic to them while they're sitting in their cars at the gate waitin' to get in 'cuz they're already late and the best bet to catch the next set would be to hop the fence but then you can guess what happens next. you find yourself at a show called casemaker that infiltrated by all these mutherfuckin fakers the next thing you know you're catchin all these headachs they took your mary jane so you can't stop the achin but whether or not it's bank i'm makin it's hot i'll be there rockin the spot pickin all the rottin shit up, i know you may never touch a maggot in your life but to me it matters i know that it ain't right for you to leave this place with your junk in my face so just bag it, the earth can't handle it the rest of us can't stomach and stand for it. so get up off your ass and pick up all your trash i know that you cats aren't used to all of that but it's what got to happen if you want to fit 6 billion people on this planet but don't fret when i'm out there working a sweat placin a bet on who picks up the next poopy tent cuz nothin excites hypes or sikes me more then seein my own human race disgraced an unnatural form.

From Lothlorien History: Fall 1990 - Summer 1995
July through November 1994: Eric Ongerth needs a place to live after graduating and moving out of room 207. He awakes one summer night with a feverish, chocolate-powered dream of how to suspend a home in the redwood tree. Soon a one-room cabin begins to take shape in the tree right across from the third flor of North House. Working on it six days a week, Eric soon has a place to stay, and lives out a most beautiful year among the birds and squirrels, waking every day to brilliant sunlight, wooden beams, and the grind of traffic at the Prospect/Channing intersection.

By 1995 the treehouse grows infamous within the coop system and those members of other houses who eat the most granola and spend the most time drumming in the forest come and visit. Central maintenance personnel do their best to pretend it doesn't exist. The Daily Cal places the treehouse #1 on a list of "best places for a date".

From Wikiversity:Decision Science
To make decisions, you need to be very smart and think ahead...no, wait....

From Enriquesjokes
Enrique's joke consist of a simple formula. Simply take a racist term, add a profane word, and follow it by some form of excrement. (ie; Wop's like to fuck crap). If this fails, then shout a string of obscenities, grab your penis, or pretend to hump something invisible.

Slim
One of the most respected ranch workers, with strong leadership skills. MOOOOOOOOO!

From Getting a date/Cautionary note
Getting a date, or worse yet, falling in love, can change the way you see the whole world. You may never be able to go back to the way you saw it before. You may even skip against your will, in public, where others can see you. Don't say you weren't warned.

More bad jokes
fr:zh:ar:ms:de:q:ja:wikt:es:simple:m:b:WB:BJ --Kernigh 05:52, 4 March 2006 (UTC)

Excerpt from Wikijunior Languages/Galactic Basic
Galactic Basic uses the "Aurabesh" script of writing. The Aurabesh look very different from standard English letters, but they still sound exactly like English letters. ... In real life, this language is English, but in the fictional Star Wars world, billions of people speak Galactic Basic, which is commonly called "Basic". ... Galactic Basic is spoken just like English. In fact, speaking English is virtually speaking Basic! So any English words you know are also part of Galactic Basic.

The only difference is that they are written in the Aurabesh script.

From Minecraft resource gathering/Crops
Diarrhea can be harvested directly from other people, by giving them laxatives and eye drops. The best way to harvest diarrhea is with an anal funnel. Once diarrhea is harvested, it can be stored in drums and later used to make diarrhea dick jizz. Diarrhea dick jizz is made by pumping diarrhea into a dick hole until it can’t hold any more diarrhea, then jacking off until diarrhea jizz shoots everywhere. Many famous artists have created renowned masterpieces with diarrhea dick jizz this way, by collecting different types and colors of diarrhea.

From Minecraft resource gathering/Elliot Harkness
You get Elliot Harkness by mining Stupid Ore with your fist. You can get Stupid Ore by smelting Dirt.

Use
Elliot Harkness gives you bad tips about Minecraft. I know who this Elliot Harkness is

title: User:Garfieldcat1978/BJADON


text: User talk:Yibanathi Ngcupe

title: User talk:Yibanathi Ngcupe


text:
User talk:Slava Ukrajini Heroyam Slava

Print version still broken
The print version of Kittypet's Guide To Warrior Cats is still broken.Garfieldcat1978 (discuss • contribs) 22:37, 25 February 2023 (UTC)
 * , I noticed that. Unfortunately I don’t have any more ideas how to fix it. I tried something which I thought might work, but I didn’t. Maybe editing it without changing anything and publishing it will refresh it, but if it doesn’t work, then idk how to fix it. You might want to contact someone else. Sorry. -Slava Ukrajini Heroyam Slava (discuss • contribs) 13:01, 26 February 2023 (UTC)
 * Mbrickn has already done that, and it didn’t work. I’m not sure how to fix it. -Slava Ukrajini Heroyam Slava (discuss • contribs) 13:02, 26 February 2023 (UTC)
 * Requesting that we delete the print version and remake it. Garfieldcat1978 (discuss • contribs) 16:44, 27 February 2023 (UTC)
 * I’m not sure if deleting it, and then remaking it will help fix the problem, however submitting a request will help gain attention from more experienced users who might fix it. However it might be a better idea to send a post in Wikibooks:Reading room/General. -Slava Ukrajini Heroyam Slava (discuss • contribs) 17:36, 27 February 2023 (UTC)
 * , I have published a post there, but I’m not sure if an automatic printable version fits for the book you are creating. An automatic print version just takes all the link from the main page and displays them. In this book each of the pages has subpages which will not be included in the automatic print version. Creating a manual print version by embedding the pages might be preferable. See example Windows XP/Printable version. -Slava Ukrajini Heroyam Slava (discuss • contribs) 17:43, 27 February 2023 (UTC)
 * , I have fixed the print version by embedding the pages instead of using the automatic template. Notice that when you create the subpages, you will have to embed them yourself, though the automatic template would not embed them at all. -Slava Ukrajini Heroyam Slava (discuss • contribs) 17:30, 28 February 2023 (UTC)
 * By subpages I mean for example the page about ThunderClan. -Slava Ukrajini Heroyam Slava (discuss • contribs) 17:31, 28 February 2023 (UTC)

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This project may be postponed if necessary. You can read the schedule at wikitech.wikimedia.org. Any changes will be announced in the schedule. There will be more notifications about this. A banner will be displayed on all wikis 30 minutes before this operation happens. Please share this information with your community.

Trizek (WMF) (m:User talk:Trizek (WMF)) 21:20, 27 February 2023 (UTC)

 * Mdsamad55 103.86.199.245 (discuss) 22:08, 12 May 2023 (UTC)

Garfieldcat1978 (discuss • contribs) 22:24, 27 February 2023 (UTC) You should know about this.
 * Thanks for the information. -Slava Ukrajini Heroyam Slava (discuss • contribs) 15:08, 28 February 2023 (UTC)

title: User talk:Slava Ukrajini Heroyam Slava


text:
Using and accessing MATE

Table of contents

title: Using and accessing MATE


text:
Using and accessing MATE/Sommaire

Welcome

 * 1) MATE Basic concepts
 * 2) Writer, word processing
 * 3) File manager
 * 4) Get help using MATE
 * 5) System configuration
 * 6) Introduction to the Internet

Shortcuts list

title: Using and accessing MATE/Sommaire


text:
Using and accessing MATE/Welcome

Welcome

Introduction
Welcome in the Using and Accessing MATE tutorial. This document is designed to provide low-vision persons with understanding the graphical environment concept under MATE and how it works. This book has the benefits of training where you have theorical information and practises. You can select easily topics, listen or read the explanations at your own convinience, and review them if needed.

This lesson, divided by six modules, deals with the following topics:

 * Basic MATE concepts
 * Writer, word processing
 * FIle manager
 * Get help using MATE
 * System configuration
 * Introduction to the Internet

Each module is divided by lessons. The last lesson of each module is a five-questions/answers game, about the addressed topics in the module.

FOr this book, we assume you have a computer where MATE is installed, with Compiz as window manager. The closest configuration for such prerequisities is brought by the Debian with a low-vision profile.

Some lessons include screenshots, for sighetd and low-vision persons, in order to see the screens we talk about.

You can get such screenshots in braille, in a paper document ordered by picture numbers.

As the explanations of this book are designed to low-vision and blind persons, all the lessons describe the menu and keyboard commands. The appendix is a quick reference about the keyboard shortcuts.

This tutorial is designed to be used with assistive technologies, e.g. a screen reader or a magnifier utility. That is why this is different from other tutorials as there is not mandatory and inaccessible picture, not movie.

Another appendix contains an additional help about the list of the commands provided by the Orca screen reader related to what is shown in this book. When an Orca command is usable during a topic, a footnote will refer to it.

Welcome in this tutorial for using and accessing MATE.

What are the writing conventions in this manual?
Any manual has some writing conventions to stay relevant and make the reading easier. Here:

 * 1) All the step-to-step processes and practises are in numbered list.
 * 2) Some keys are referred to by abreviations: ctrl for control, alt for the alternative key (or Meta); tab for the tabulation key.
 * 3) All the commands and cimbinations are written in lowercase and the keys are separated with a dash if pressed at the same time, e.g. ctrl-alt-down arrow. This means that you need to press alt, ctrl, and the down key, then release everything.

title: Using and accessing MATE/Welcome


text:
Raku Pottery/Creation

The creation process of Raku originated in Japan, but an American style also exists.

Some say the creation of Raku is an experimental process.

title: Raku Pottery/Creation


text:
Raku Pottery/Introduction

Raku is a form of pottery.

title: Raku Pottery/Introduction


text:
Fractals/print

How to make quality prints of 2D static images (computer graphic, non-photographic digital images), escpecially fractal images ?

To get quality print one should choose:
 * base
 * ( paper type )
 * size
 * resolution ( dpi)
 * main print method

=file =
 * type and version
 * ink limit
 * colors
 * specyfication
 * data

type

 * pdf type version 1.3.

=color=

color profile

 * ICC color profile of printig device

=base=
 * type
 * size
 * maximal ink limit

types
There are three main types of large posters:
 * Paper posters are the most common type of large poster. For indoor and outdooruse after lamination
 * Vinyl posters for outdoor use.
 * Fabric posters for indoor use.

Paper
 * GSM stands for grams per square meter and determines how heavy the paper stock is

Different paper types for posters include:
 * Gloss ( Gloss Art FSC or 150gsm ) a glossy sheen to any poster. The shiny finish encourages an eye-catching look for your poster designs and is available in six different paper weights.
 * Bond – 100% recycled and high-quality, bond paper is an environmentally-friendly poster option. It’s durable and available in two different weights at Solopress.
 * Day Glo – For a fluorescent colour scheme, day glo posters are the go-to. With a luminous effect, this paper is perfect for making a huge impression.
 * Light Box – When you’re using a back light to illuminate a poster advert, print it on light box paper. It’s the ideal method for use in cinemas, theatres and on the street.
 * 170gsm Silk

maximal ink limit
When several colors are printed on top of each other, there is a limit to the amount of ink or toner that can be put on paper. This maximum total dot percentage is referred to as either

Names

 * TIC = Total Ink Coverage
 * TAC (Total Area Coverage, pl. Suma wartości tonalnych)
 * TIL ( TOTAL INK LIMIT )

The limit depends on a number of parameters:
 * the printing process type (digital, sheet offset, web offset (heatset or non-heatset), laser printer,…) and many of it's parameters
 * the paper stock (coated or uncoated,…)

How to check total ink coverage ?

 * check settings in your program

How to avoid exceeding total area coverage ?

 * choose paper type, printing device and method and then set up appropriate ink limit in your program
 * make RGB to CMYK converion

What happens when one exceeds TAC ?

 * the ink that gets laid down last won’t attach properly to the previous layers, leading to muddy browns in neutral areas
 * the ink also won’t dry properly on the press sheets. This can cause set-off where the ink of a still wet sheet rubs off on whatever is stacked on top of it

=editing program=
 * GIMP has no CMYK
 * Krita has CMYK but can't export to pdf
 * Scribus supports professional publishing features, such as CMYK colors, spot colors, ICC color management and versatile PDF creation

=print=

Printing method

 * a litho print involves the printer making a set of 'plates' that are used to press the image to the paper. Creating these plates comes at a cost and doesn’t offer the immediacy of digital poster printing. The initial outlay can be expensive, but if you’re doing a large print run and want to output up to A1, it’s the process that offers a higher quality print and finish than digital printing.
 * Digital printing with inkjet in wikipedia or laser printers is the cheaper and quicker of the two and good for smaller print runs. If budget is an issue and you’re not being too exacting over the quality, go with digital printing. This is also fine if you're not going above A3.

printing resolution
DPI ( dots per inch)
 * 300 dpi does the trick
 * 600 dpi is good for graphics
 * 1200 dpi is ready to be sent to the company executives
 * 1440+ dpi is professional-level photographic print quality

size
How to choose poster size ? SIZE	DIMENSION Smallest	 8.5×11 in = 21.59 × 27.94 cm = minimal size of the poster Small	   11 × 17 in = 27.94 × 43.18 cm = for indoors in bars or shop windows Medium	   18 × 24 in = 45.72 × 60.96 cm = for gig and event posters Large	   24 × 36 in = 60.96 × 91.44 cm = posters hanging in exhibition halls or museums very large	27 × 40 in = 68.58 × 101.6 cm = for Movie biggest	40 × 60 in = 101.6 × 152.4 cm = for Bus Stop

How to choose image resolution ( ppi) ?
It depends on:
 * paper size
 * print resolution

Examples :

A sizes (1.413 ratio):
 * A4 Paper Poster Size: 8.5” x 11” = (21 x 29.7 cm) = 2 550 x 3 300 points ( at 300 dpi ) =
 * A3 = 420 x 297 mm = 42 x 29.7 cm = 16.54 x 11.69 in = 4 962 x 3 507 points ( at 300 dpi)
 * A2 = 594 x 420 mm = 59.4 x 42 cm = 23.39 x 16.54 in = 7 017 x 4 962 points ( at 300 dpi )
 * A1 = 841 x 594 mm = 84.1 x 59.4 cm = 33.11 x 23.39 in = 9 933 x 7 017 points ( at 300 dpi)
 * A0 = 1189 x 841 mm = 118.9 x 84.1 cm = 46.81 x 33.11 in = 14 043 x 9 933 points ( at 300 dpi)

B sizes ( 1.4 ratio)
 * B2 = 707 x 500 mm = 70.7 x 50 cm = 27.83 x 19.69 in = 8 349 x 5 907 point ( at 300 dpi)
 * B1 = 1000 x 707 mm = 100 x 70.7 cm = 39.37 x 27.83 in =
 * B0 = 1400 x 1000 mm 140 x 100 cm = 55.12 x 39.37 in =

How to compute image resolution ?

image resolution ( pixel x pixels) = paper size ( inch) x printing resolution ( dpi)

=See also=
 * How to make 2D static images (computer graphic, non-photographic digital images), escpecially fractal images for display ?

=references=

title: Fractals/print


text:
Statistics/Multivariate Data Analysis

Multivariate Normal
The multivariate normal is just an extension of the normal distribution to the multivariate case. The simplest definition of the multivariate normal distribution can be given as follows:

At first glance, the definition seems rather abstract and esoteric. After all, the univariate normal distribution has a specific form of density and a specific characteristic function, both of which are mathematically valid characterisations of any probability distribution. However, this kind of definition is necessary to deal with the case where $$\Sigma$$ is not strictly positive definite. In the case where $$\Sigma$$ is positive definite, it can be shown via Gauss-Markov theorem that the density function of $$\mathbf{X},\ f_{\mathbf{X}}(\mathbf{x})=\frac{1}{\sqrt{2\pi}|\Sigma|^\frac{1}{2}}e^{-\frac{1}{2}(\mathbf{x}-\mu)^T\Sigma^{-1}(\mathbf{x}-\mu)}$$. However, this will not be true when $$\Sigma$$ is singular, as in that case the density function will not exist. But a definition based on the characteristic function will still work. A piecewise density function can still be derived based on the eigenvalues of $$\Sigma$$, but it is not a true density.

Matrix-variate Normal
We will first need to develop some notation. Let $$X_{m\times n}$$ be a matrix with columns $$c_{(1)}, c_{(2)},\ldots,c_{(n)}$$. Then we define the column vector $vec(X):=\begin{bmatrix} c_{(1)} \\ c_{(2)} \\ \vdots\\ c_{(n)} \end{bmatrix}$, and we call it the vectorisation of $$X$$.

The reader here should notice that this is simply imposing a normal distribution on the vectorisation of $$X$$. Thus, many of the results that are true for multivariate normal random vector will also be true for the vectorisation of matrix variate normal random variable.

Now that we have a definition of the multivariate and matrix-variate normal distribution, our next aim should be to find a similar analogue of the univariate $$\chi^2_{(p)}$$ distribution with $$p$$ degrees of freedom and Student's $$t$$ distribution, both of which are very closely related to the univariate normal distribution. We know that if $$X_i\sim\mathcal{N}(\mu_i,\sigma^2_i)\ \forall i\in\{1, 2,\ldots n\}$$ then $$\sum_{i=1}^n\frac{(X_i-\mu_i)^2}{\sigma^2_i}\sim\chi^2_{(n)}$$. What would be an analogue of this for the multivariate case?

Wishart Distribution
Although there does exist a form of density for the Wishart distribution, it is not necessary to prove most of the results we will require. An important thing to note, however, is that if $$S$$ follows a Wishart distribution, then $$\frac{\mathbf{a}^TS\mathbf{a}}{\mathbf{a}^T\Sigma \mathbf{a}}\sim\chi^2_{(n)}$$. This result can be easily proved by multiplying $$S$$ on the left and right by $$\mathbf{a}^T$$and $$\mathbf{a}$$, and then using the fact that $$\mathbf{a}^T\mathbf{X}\sim \mathcal{N}(\mathbf{a}^T\mu, \mathbf{a}^T\Sigma \mathbf{a})$$.

Methodology

 * 1) Principal Component Analysis
 * 2) Canonical Correlation Analysis

title: Statistics/Multivariate Data Analysis