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The Mandelbrot set contains infinitesimally narrow filaments that branch and twist along its boundaries. These jagged features, called dendrites for their visual similarity to tree roots, remind me of lightning on a stormy night.
I generated this colorful rendering of the Mandelbrot set shortly after I learned of this great man’s passing: http://mathcadworksheets.blogspot.com/2010/11/generate-colorful-images-of-mandelbrot.html
Nifty.