Henon Map Real Parameter Space by Karl Papadantonakis

The following images all created using SaddleDrop

key (above)

• yellow: all critical points escaped

• red or black: some critical points did not escape (approximately the horseshoe locus compliment)

• black: no critical point escaped (approximately the connectedness locus)

• gray curve: outline of period 1 sink locus (should be painted red inside)

• white: inability to follow critical points continuously

below: same region, with more holes in horseshoe locus revealed

below: connectedness locus (black in top image) zoomed around c=-2, a=0 (the tip of the Mandelbrot set). We have named the large revealed island "Australia"

Below: blowup of Australia

See also: Complex parameter space pictures

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