I've just asked sage to expand g/g' for the triply iterated Mandelbrot map, and put it into XaoS: $ xaos -speed 3.5 -maxiter 500 -palettef -anti -usrform '(((z^2+c)^2+c)^2+c)/8*((z^2 + c)^2 + c)*(z^2 + c)*z'pic.twitter.com/eWkPVF203N
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I've just asked sage to expand g/g' for the triply iterated Mandelbrot map, and put it into XaoS: $ xaos -speed 3.5 -maxiter 500 -palettef -anti -usrform '(((z^2+c)^2+c)^2+c)/8*((z^2 + c)^2 + c)*(z^2 + c)*z'pic.twitter.com/eWkPVF203N
Gee, this formula is much more weird than I was prepared to see. Owen? Are you seeing this? Owen!? That mu-set looks twisted along its cardioid. The seahorse valley has an antenna, and there's an egg around the straight p=2 antenna! Welp.
Indeed - the 3 nonzero roots of the polynomial ((0^2+c)^2+c)^2+c =0 - i.e. forcing 0 into a cycle of length 3.
This is mathematical balloon art.
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