Is there a difference between a fractal dimension, and "human
imperfection" when creating jewelry? What distinguishes the
acceptable fractal dimensions from other imperfections of a man
made object; or is imperfection just a poorly executed fractal
Fractal is an object made of self-similar, but smaller objects.
Take a broccoli. Broccoli is fractal. We can take a bunch of
broccoli and start taking it apart. We quickly notice that all parts
regarding of size look alike. Not the same but similar. That is
necessary characteristic for fractal.
Is there an ugly broccoli ? No. Is there beautiful broccoli ? No.
Broccoli is simply interesting. One can study it's shape for hours
and will keep finding variations. Nothing is the same, but similar,
and every element will have the same fractal dimension.
What is fractal dimension? Staying away from mathematics, draw a
square on the paper. We can easily compute the area and the perimeter
of this square.
Replace each side of the square with two lines joined at some angle
What just happen is that area of the square become smaller, but the
perimeter became larger. We can continue this process forever and if
we do, we observe that length of the perimeter is infinite, but the
area is not. Area would become smaller and smaller tending to some
finite quantity. This is actually quite remarkable.
We have perimeter of infinite length encompassing finite area.
Going back to broccoli, is it possible to exactly measure the
surface of the broccoli ? Absolutely not, but we can measure the mass
and there by the volume by simply weighing it.
What about jewellery? Every article of jewellery has certain feel
about. Some call it soul, which is fine. Formally it is perception of
it's fractal dimension. As long as "imperfections" have the same
fractal dimension, they will look like they belong.
To understan this study the work of Auguste Rodin. His surfaces
always rough and unfinished, but they belong. Take technique like
pave. If we examine cut by cut; stone by stone, - there is nothing
perfect about it. Nevertheless, some pave looks like it contribute to
the article of jewellery, and some looks like it been glued on top of
article by mistake. This is what is called "setter's talent", or we
can call it fractal intuition.
One more example. How does an artist make hair look like it has
It is not possible to draw every single hair. What about sculptor
who works in marble ? Try to convey this feeling of wind playing with
hair in CAD.
Good luck if you decide to try. Nevertheless, it is accomplished by
thousands of artists on daily basis. A few strokes of pencil, or few
cuts with chisel and it is done.
On some level artistic talent is an ability to recognize and
reproduce fractal dimension of and object. That is why caricature
works. Caricature and it's object do not look alike, but they have
the same fractal dimension.