Mandelbrot set but with Manhattan distance calculations.pic.twitter.com/7c3aQJizpC
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Mathematics Sorceror (sensory alchemist) at the Arctangent Transpetroglyphics Algra Laboratory (ATAL), I transmute mathematics into living rainbows.
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Mandelbrot set but with Manhattan distance calculations.pic.twitter.com/7c3aQJizpC
Ok, this is totally not what @graveolens was getting at (soon!?), but here is the same sketch, but now the points in the mandelbrot set are colored based on how much they travel throughout the trip. I.e. Cab distance.pic.twitter.com/AV7fi0bCgd
Unclear, @mathzorro, @hollykrieger: I suggested to @dandersod that we keep track of zigs and zags for the Manhattan itinerary which he used to color this. I know of very few coloring schemes which automagically color different components differently.
And then I got to thinking: with well-defined zig and zag conditions, at least relative to whatever pixel system (which gets us integets) its plotted in, unroll it and you have a lattice path. ... Hey, don't the Catalan numbers appear in Mandelbrot polynomials?
https://mathoverflow.net/questions/247038/can-we-define-the-mandelbrot-set-in-terms-of-the-generating-function-of-the-cata … If those paths can be unrolled sensibly, the associated Young diagrams and integer partition congruences might carry over to eta function identities. (and that's all I have for now)
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