newton_min_angle_starfish.cpp File Reference

Draw a Newton Fractical. More...

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Detailed Description

Draw a Newton Fractical.

Author

Mitch Richling https://www.mitchr.me

Standards

C++20

Copyright

Copyright (c) 2024, Mitchell Jay Richling https://www.mitchr.me All rights reserved.

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Details

We do the standard Newton iterations, but we keep track of the minimum phase angle difference between the three bisectors between the roots. The distances are used to set the r, g, b channels (i.e. distance to root 1/2 bisector is r, root 1/3 bisector is g, and root 2/3 bisector is b).

The standard Newton fractal is generated from \( f=z^2-1 \). This function is continuous on the entire complex plain. What do we get if we add poles in imaginary axis mirror locations of the roots? i.e. for each root \( x+iy \) of \( f \), we add a pole at \( -x+iy \)? The corresponding function is:

\[ f=\frac{z^3-1}{z^3+1} \]

Definition in file newton_min_angle_starfish.cpp.