About the fractal diagram

  The fractal is the concept which was devised  about 20 years before by
theMandelbrot of the French. Announcement by the way, there are a lot of
ones  which  are funny with the  Mandelbrot set and the  Julia set being 
famous  especially in the  diagram to  make with the  computationof  the
computer. Also, how many kind the software for the personalcomputer, too,
is is announced.

The Mandelbrot set

 Probably, it is a representation rank, although mandelbrot set figure is
 complicated and it is interesting of complex dynamics system. Even if it
 expands this figure with self-similarity repeatedly, it is a wonderful 
figure in which the same figure as origin appears. This figure,
         Z(n+1) = Z (n) * Z (n) +G    (both Z and G are complex numbers)
 It can express.
When initial value is Z(0) =0, a set of constant G which |Z(n) | does not
 emit infinitely is called mandelbrot set.
A black portion is mandelbrot set.
This portion is converged.
An interesting figure appears into a boundary portion.

Julia set

       Z(n+1)= Z(n) * Z(n) + G   (both Z and G are complex numbers)
 A set of initial value Z(0) which is set and |Z(n)| does not emit infinitely
is called filling Julia set. The boundary of this set is called 
Julia set.
It has the same character as the mandelbrot set.

Filling Julia set Filling Julia set

Fun of a figure

 When actually calculating with a personal computer, repetition
calculation is carried out and it is made to converge. Even if
it calculates repeatedly and it reaches the number of times of
the close until it surpasses a certain value, when not emitting,
it shall converge. At this time, if it colors according to the
speed of emission, a beautiful pattern will appear.
It is this figure colored according to the
speed of emission of the surroundings of the
above-mentioned filling Julia set.
Repetition time n=100
Mathematically, a color is unrelated. Then, according to the speed of
emission, it colors suitably. If this coloring method is changed, it
will become the figure from which the same figure completely also
differed.It changes variously by the method of the program of a personal
computer. Moreover, if the judgment formula which judges convergence
is changed, a pattern will change. Furthermore, pleasant work discovers
the place by which an interesting figure may be made and the interesting
figure is hidden, also by changing the original formula.
Although looking at the figure made is also pleasant, it is still pleasant
to draw a figure using a personal computer.

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