newton_min_root.cpp File Reference

Draw a Newton Fractical – color by orbit distance from roots. More...

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Detailed Description

Draw a Newton Fractical – color by orbit distance from roots.

Author

Mitch Richling https://www.mitchr.me

Standards

C++20

See also

https://www.mitchr.me/SS/newton/index.html#min_root_d

Copyright

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

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.
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Details

We do the standard Newton iterations, but we keep track of the minimum distance from the roots by any iterate of the orbit. Then we use the two largest minimum distances to color the pixel. The distances are used to set the r, g, b channels (i.e. distance to root 1 is r, root 2 is g, and root 3 is b). Closer is a brighter color. By using the two largest and omitting the third distance, the color represents how close the orbit got to the roots to which it didn't converge.

Definition in file newton_min_root.cpp.