RSSmandelbrot

Efficent automated Julia morphing

Nucleus finding, Misiurewicz point finding, and a bit of guesswork, combine for successful O(period) automatic Julia morphing.

Deep zoom rendering cost

Some conclusions about perturbation techniques.

Approximate self-similarity

Approximate self-similarity of baby Mandelbrot sets.

Asymptotic self-similarity

Asymptotic self-similarity about Misiurewicz points in the Mandelbrot set.

Filtered atom domains

Highlighting previously invisible periodic properties in the Mandelbrot set.

Periodicity scan

Finding periodic points in the Mandelbrot set to make annotated images.

Kalles Fraktaler with GMP

Using third-party libraries for acceleration.

Inflector Gadget v0.2

Double precision using OpenGL 4 to avoid postpone ugly artifacts.

Inflector Gadget

Inflection mapping for complex quadratic polynomials.

Finding parents in the Farey tree

An application of the extended Euclidean algorithm.

Vector Buddhabrot

Tracing the boundaries of hyperbolic components.

Simpler series approximation

When thinking a bit harder beats elaborate computer code.

Julia morphing symmetry

Rotation numbers in angled internal addresses are significant.

Two spirals out...

Sculpting patterns in the Mandelbrot set.

Misiurewicz domains

An extension of atom domains to preperiodic points.

mightymandel v16

Sliced rendering, improved glitch correction, reduced video memory usage, and more.

Calendar 2015 - Dandelion

A shadow of the Mandelbrot set formed by periodic external rays.

External angles of Misiurewicz points

Numerical investigations, hoping for a combinatorial revelation.

mightymandel v15

Big bad bugs been debugged, and nifty features added.

mightymandel updates galore

Automatic glitch correction, zoom sequence rendering, tiled rendering for high resolution or anti-aliasing, ...

Automatically finding external angles

Trace a number of probe points in the atom domain.

Navigating in the hairs

Around embedded Julia sets in the Mandelbrot set.

Stretching cusps

Conformal mapping using Möbius transformations.

Atom domain size estimation

A series of approximations result in a simple formula.

A roadmap for distributed Mandelbrot set rendering

Some notes on various aspects of design and potential implementation.