mathr / blog / #


Perturbing Nova

Affine-conjugation to move the critical point to 0 to avoid precision loss.

External ray tracing

In which various initial guesses for Newton's method are tested.

Ultimate Anti-Buddhagram

Two ways of rendering the 4D Mandelbrot/Julia/Buddhabrot hologram.

Newton's method for periodic cycles

Reject lower periods, and iteratively perturb a known cycle along a path.

Newton's method for periodic points

Rejecting lower periods by division, instead of checking later.

Calendar 2015 - Two Beetles Meet Where Land Meets Sky

Distance estimated Newton fractal for a rational function with zeros at {1, i, -1, -i} and poles at {-2, 2}.