ikeda_attractor.cpp File Reference

Draw an Ikeda map fractal. More...

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Detailed Description

Draw an Ikeda map fractal.

Author

Mitch Richling https://www.mitchr.me

Standards

C++20

See also

https://www.mitchr.me/SS/sic/index.html

Copyright

Copyright (c) 1988-2015, Mitchell Jay Richling https://www.mitchr.me All rights reserved.

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Details

The one parameter Ikeda map is given by the following iteration:

\[ \begin{eqnarray} t_n & = & \frac{2}{5} - \frac{6}{1+x_n^2 + y_n^2} \\ x_{n+1} & = & 1 + u (x_n\cos(t_n) - y_n\sin(t_n)); \\ y_{n+1} & = & u (x_n\sin(t_n) + y_n\cos(t_n)); \\ \end{eqnarray} \]

Where \( u \ge \frac{3}{5} \) is a parameter.

We compute SGSIZ^2 paths for the attractor. The initial condition for each path is pulled from a SGWID wide grid centered at the origin. We compute MXITR steps for each path, and plot the steps after the DRTHS's iteration.

Definition in file ikeda_attractor.cpp.