You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
a cauliflower is a variety of cabbage with an edible head of condensed flowers and flower stems .
it is a form of cabbage in the mustard family , consisting of a compact terminal mass of greatly thickened , modified , and partially developed flower structures , together with their embracing fleshy stalks .
this terminal cluster has been known as a typical fractal among living organisms@xcite .
it is clear that the dimensionality of a fractal is the most fundamental concept of fractal analysis .
nevertheless , the fractal dimension of a white cauliflower has not known yet .
grey and kjems discussed the fractal dimension of a cauliflower , and they just suggested the possibility that the fractal dimension of a cauliflower could be larger than that of a broccoli@xcite .
romera et .
al . suggested a mathematical model of a cauliflower as a sequence of a baby mandelbrot set @xcite , and its fractal dimension was not obtained , either .    in this article , we measure the fractal dimension of the cross - section of a white cauliflower .
then , the fractal dimension of the bulk cauliflower is introduced .
next , we create a mathematical model for the cauliflower , and compare it with our experimental measurement .
the condition of creating the fractal in our mathematical model is discussed , too .
there are many definitions of fractal dimensions , and the basic concept in our model has almost the property as follows : let us introduce that @xmath1 is a measurement scale , and that the measurement is @xmath2 , then the fractal dimension @xmath3 of a set @xmath4 is determined by the power law @xmath5 if @xmath3 is a constant as @xmath6 , @xmath4 has a dimension of @xmath3 .    the term
 capacity dimension " or  box - counting dimension " is most widely used , because it can be easily applied to fractal objects .
it is defined as @xmath7 where @xmath8 is the smallest number of sets of diameter at most @xmath1 which can cover @xmath4@xcite .
fractal objects embedded in one- or two - dimension are easy to measure relatively compared to other higher dimensions , but most of fractals in nature that are embedded in three dimensions is difficult to measure even in the capacity dimension . however , the dimensions of a cross - section is generally known to be related with that of the bulk .
let us think of a bulk of three dimensions , and assume the dimension of its cross - section is two , that is , it is 2/3 of the bulk .
we can propose an _
ansaz _ from the above property : let @xmath9 be a fractal dimension of a cross - section embedded in two dimensions .
then , the fractal dimension of the bulk imbedded in three dimensions can be written as @xmath10 where @xmath11 represents every possible cross - section . as the fractal dimension of the cross - section is independent of directions , eq .
( [ 30 ] ) is simply written as @xmath12 .
we prepared several white cauliflowers of about @xmath13 in mass and @xmath14 in diameter .
we cut half of them in horizontal ( h ) direction , and the other half in vertical ( v ) direction .
then , we scanned the cross - section by a scanner and read the image into black and white in fig . 1 . here , the two figures by the two perpendicular directions look totally different .
next , we read the image into matrix of numbers .
the numbers of the matrix are the reflectivity of each pixels .
the black backgrounds produces 0 s , and the white images produce large numbers .
let us call the non - zero number 1 for convenience .
the size of the matrix is about @xmath15 .
note that the size of a pixel is an order of 100@xmath16 .    in order to measure the fractal dimension of the cross - sections in eq .
( [ 20 ] ) , we count the non - zero numbers by the box - counting method .
it becomes the smallest number of sets to cover the white images by @xmath17 . in a half reduction procedure of the matrix ,
a @xmath18 component becomes 1 if it contains any non - zero number , otherwise it becomes 0 .
then , the number of 1 s becomes the smallest number of sets to cover the white images by @xmath19 . and so on .
in the reducing steps in half , that is @xmath20 , the conversion from the reduced matrices to images is plotted in fig . 2 for the first four steps .
we see that the basic structure of the cross - sections remains unchanged .
3(a ) is the log - log plot for the h - direction , and fig .
3(b ) is for the v - direction .
we plotted it for a couple of different cauliflower samples .
the slopes are the capacity dimensions of the cross - sections .
surprisingly , we found the two slopes for different directions are very similar .
it is @xmath21 . repeating the procedure for different white cauliflowers , we observed similar values of @xmath22 as @xmath23 for the two different directions
therefore , from eq .
( [ 30 ] ) we predict that the capacity dimension of the white cauliflower is about 2.8 .
converting a fractal found in nature into a corresponding mathematical model is a hope of a theorist , but most of the work is far away from the real world or extremely complicated in analysis .
the modeling of nature should be as simple as it can , and at the same time , it should contain the basic structure of nature .
furthermore , if some physical quantities of the model can match the real systems , it will guarantee more credits to the mathematical model .
we modeled the cross - section of a cauliflower in v - direction as a rectangular tree that has three equilateral sides in fig .
this is the simplest model of a self - similar set that has a single scale factor @xmath24 .
note that the cross - section of a broccoli in v - direction has modeled into a self - similar set of triangular tree or pythagoras tree @xcite .
the the scale factor @xmath24 of the rectangular tree in fig .
4 have the following relation @xmath25 where @xmath26 is the angle of the rectangular tree .
downsizing the tree by a ratio @xmath24 , it creates three branches .
therefore , the fractal dimension of fig .
4 is @xmath27    the areas of the rectangular tree have the following series @xmath28 where @xmath29 . because the fractal is the limit of the series
, it should converge as @xmath30 increases .
the condition of convergence of the series is @xmath31 , or @xmath32 .
it is clear from @xmath33 .
this condition corresponds to @xmath34 by eq .
( [ 40 ] ) .
since the @xmath9 in the cauliflower is 1.88 , the scale factor @xmath24 and the angle @xmath26 in the model is obtained as 0.56 and @xmath35 from eqs .
( [ 40 ] ) and ( [ 45 ] ) .
we recognize that the cross - section in v - direction of the cauliflower is pretty close to two dimensions .
as the @xmath26 approaches @xmath36 , the dimension of the tree goes to two because the limit bents to cover the two dimensional surface . on the other hand ,
as the @xmath26 approaches @xmath37 , the dimension of the tree goes to one because the limit goes to a long rod .
the head of the real cauliflower is rounded not like the model in fig .
4 . it gives a possibility that the real cauliflower is not a self - similar set of single scale factor , but a set of multi - scale factors .
we measured the fractal dimension of the cross - section of a white cauliflower by the direct scanning method .
it was @xmath0 , and almost independent of the directions of the cross - sections . from these results
, we predict that the fractal dimensions of the bulk cauliflower is about 2.8 .
we created a mathematical model for the v - direction of a cauliflower with only one scale factor .
it is a rectangular tree of three equilateral sides .
we suggested the condition of creating fractals in our model , and we showed that the angle of the model is 67 degrees and the scale factor is 0.56 comparing with experiment .
this method of a scanning cross - sections and mathematical model from a polygonal tree can be widely applied to many complex bulk fractals in nature .
b. mandelbrot , _ the fractal geometry of nature _ ( freeman , new york , 1977 ) . f. grey and j. k. kjems , physica d. * 38 * , 154 ( 1989 ) .
m. romera , g. paster , g. lvarez , and f. montoya , computers @xmath38 graphics , * 28 * , 437 ( 2004 ) .
k. falconer , _ fractal geometry _
( john wiley & sons , new york , 1990 ) .
k. falconer , _ techniques in fractal geometry _ ( john wiley @xmath38 sons , new york , 1996 ) .
peitgen , h. jurgens , and d. saupe , _ chaos and fractals _ ( springer , new york , 1992 ) p.126 .
the fractal structure of a white cauliflower is investigated by box - counting method of its cross - section . 
 the capacity dimension of the cross - section is @xmath0 independent of directions . from the result 
 , we predict that the capacity dimension of the cauliflower is about 2.8 . 
 the vertical cross - section of the cauliflower is modeled into a self - similar set of a rectangular tree . 
 we discuss the condition of the fractal object in the tree , and show that the vertical cross - section has an angle of 67 degrees in our model .