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.

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. |

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 |

(G=0.3+0.02i) | (G=0.35+0.35i) |

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 (G=0.3+0.02i) |

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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