
Newton & Halley
Sinh Cubic Ember
Newton Fractal
Newton's method applied to f(z) = sinh(z) - z^3, framed 20 wide on the origin. The function is odd, so the basin of -r is the reflection of the basin of r and the image has exact 180 degree symmetry. Chroma is keyed to the modulus of the captured root, which preserves that symmetry, and luminance is keyed to the step count. A cos(2 pi count) ripple grains the flat basin interiors without touching the lace.