Mandelbrot set: Difference between revisions

The Mandelbrot set is represented using Normal Maps and Stripe Average Coloring by Jussi Härkönen (cf. Arnaud Chéritat: [https://web.archive.org/web/20180127235406/https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set#Normal_map_effect ''Normal map effect'']). See also the picture in section [https://web.archive.org/web/20180127235406/https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set#Mixing_it_all ''Mixing it all''] and [https://www.shadertoy.com/view/wtscDX Julia Stripes] on Shadertoy. To get a stripe pattern similar to that of Arnaud Chéritat, one can increase the ''stripes'', use ''cos'' instead of ''sin'', and set the colormap to ''binary''.

The Mandelbrot set is printed with smooth colors. The ''e^(-|z|)-smoothing'', ''normalized iteration count'' and ''exterior distance estimation'' algorithms are used with NumPy and complex matrices (see Javier Barrallo & Damien M. Jones: [http://www.mi.sanu.ac.rs/vismath/javier/index.html ''Coloring Algorithms for Dynamical Systems in the Complex Plane''] and Arnaud Chéritat: [https://web.archive.org/web/20180127235406/https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set#Boundary_detection_methods_via_distance_estimators ''Boundary detection methods via distance estimators'']). Partial antialiasing is used for boundary detection.

The Mandelbrot set is represented using Normal Maps and Stripe Average Coloring by Jussi Härkönen (cf. Arnaud Chéritat: [https://web.archive.org/web/20180127235406/https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set#Normal_map_effect ''Normal map effect'']). Note that the second derivative (ddZ) grows very fast, so the second method can only be used for small iteration numbers (n <= 400). See also the picture in section [https://web.archive.org/web/20180127235406/https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set#Mixing_it_all ''Mixing it all''] and [https://www.shadertoy.com/view/wtscDX Julia Stripes] on Shadertoy. To get a stripe pattern similar to that of Arnaud Chéritat, one can increase the ''stripes'', use ''cos'' instead of ''sin'', and set the colormap to ''binary''.