Category Archives: Art Work

Chaos Esthétique

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Drawing fractal by hand is tedious at best and close to impossible at worst. With the help of a CAS program, all you need is a few lines of code with a for-loop operation.

The fractal structure in Fig. 1 is generated from Gumnowski-Mira chaos model

\begin{cases} F(x)=a x+{{2(1-a)x^2} \over { 1+x^2}} \\ x_{n+1}=y_{n}+F(x_{n}) \\ y_{n+1}=-x_{n} +F(x_{n+1}) \end{cases}

by Omega CAS Explorer.

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Fig.1 a=0.31, (x_0, y_0) = (12, 0)

Replace the term x_n by -bx_n with b = 0.9998, the result is shown in Fig. 2.

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Fig.2 a=0.7, (x_0, y_0) = (15, 0)

 

 

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