feather.cpp File Reference

The feather fractal. More...

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Detailed Description

The feather fractal.

Author

Mitch Richling https://www.mitchr.me

Standards

C++20

Copyright

Copyright (c) 2025, Mitchell Jay Richling https://www.mitchr.me All rights reserved.

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Details

I learned about the "duck" or "feather" fractal from an old blog post: https://algorithmic-worlds.net/blog/blog.php?Post=20110227

The idea is to iterate a function a fixed number of times for each point in the complex plane, and then color that point according to the magnitude of the mean of the orbit points. In this case we iterate the log of the "iabs" function:

\[ \log\left(\Re(z)+\vert\Im(z)\vert+c\right) \]

Coloring by the magnitude of the final iterate is interesting; however, I think it's even more interesting to color by the final iterate relative to the initial condition. Another interesting choice is to color by the relative argument.

Definition in file feather.cpp.