Chaos Esthétique

Screen Shot 2017-10-11 at 10.56.25 PM.png

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.

Screen Shot 2017-10-11 at 10.17.12 AM.png

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.

Screen Shot 2017-10-11 at 11.21.34 AM.png

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

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s