Mandelbrot set: Difference between revisions
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===Normal Map Effect, Mercator Projection and Perturbation Theory=== |
===Normal Map Effect, Mercator Projection and Perturbation Theory=== |
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This is a translation of the corresponding Python section. The Mandelbrot set is represented by distance estimation and normal maps using complex matrices (cf. Arnaud Chéritat: [https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set#Normal_map_effect ''Normal map effect''] |
This is a translation of the corresponding Python section: see there for more explanations. The Mandelbrot set is represented by distance estimation and normal maps using complex matrices (cf. Arnaud Chéritat: [https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set#Normal_map_effect ''Normal map effect'']). |
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<syntaxhighlight lang="julia">using Plots |
<syntaxhighlight lang="julia">using Plots |
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gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200) |
gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200) |
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savefig("Mercator_Mandelbrot_zoom.png")</syntaxhighlight> |
savefig("Mercator_Mandelbrot_zoom.png")</syntaxhighlight> |
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For deep zoom images it is sufficient to calculate a single point with high accuracy. A good approximation can then be found for all other points by means of a perturbation calculation with standard accuracy. Rebasing is used to reduce glitches. See [https:// |
For deep zoom images it is sufficient to calculate a single point with high accuracy. A good approximation can then be found for all other points by means of a perturbation calculation with standard accuracy. Rebasing is used to reduce glitches. See [https://fractalforums.org/fractal-mathematics-and-new-theories/28/another-solution-to-perturbation-glitches/4360 Another solution to perturbation glitches] (Fractalforums) for details. See also the image [https://www.flickr.com/photos/arenamontanus/3430921497/in/album-72157615740829949/ Deeper Mercator Mandelbrot] by Anders Sandberg. |
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<syntaxhighlight lang="julia">using Plots |
<syntaxhighlight lang="julia">using Plots |
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gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200) |
gr(aspect_ratio=:equal, axis=true, ticks=true, legend=false, dpi=200) |