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Atom domains and Newton basins

A counter-example to a conjecture.

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}.

Newton's method for Misiurewicz points

Rejecting lower preperiods instead of checking later.

Practical interior distance rendering

Using Newton's method.

Perturbation glitches

Rebasing from a reference point.

Mandelbrot Notebook

Handwritten notes on various properties.

Ultimate Anti-Buddhabrot

An xmas present for someone special.

Distance estimation for Newton fractals

Derived from distance estimation for Julia sets.

Preperiodic Mandelbrot set Newton basins

finding tuned branch points

Mandelbrot set Newton basins

speeding up external ray tracing

Fractal Juggling

Fractal Juggling