mathr

An implementation of someone else's paper.

How to determine the number of Misiurewicz points of a given (pre)period in the Mandelbrot Set.

A collection of rules for deriving perturbed iterations.

Do the same for Misiurewicz domains as has recently been done for atom domains.

Coordinates within an atom domain surrounding a periodic nucleus in the Mandelbrot set.

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

Lots of structure and subtle variety.

Some conclusions about perturbation techniques.

Approximate self-similarity of baby Mandelbrot sets.

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

Borrowing from Mandel's "algorithm 9".

Worst-case guess improved by a factor of 8.

Highlighting previously invisible periodic properties in the Mandelbrot set.

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

Using third-party libraries for acceleration.

Double precision using OpenGL 4 to avoid postpone ugly artifacts.

Inflection mapping for complex quadratic polynomials.

How they did it, as far as I can tell.

An application of the extended Euclidean algorithm.

A familiar picture emerges.

Notes on a conjecture of Aaron Klebanoff.

Tracing the boundaries of hyperbolic components.

Haskell compiled to JavaScript with GHCJS.

When thinking a bit harder beats elaborate computer code.

Rotation numbers in angled internal addresses are significant.

Parallel loops for coefficient recursions.

Extrapolating external angle patterns

Sculpting patterns in the Mandelbrot set.

An extension of atom domains to preperiodic points.

Rejecting lower preperiods instead of checking later.

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

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

Numerical investigations, hoping for a combinatorial revelation.

Big bad bugs been debugged, and nifty features added.

Lots of changes in a short space of time.

Sometimes simple approaches are better.

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

Trace a number of probe points in the atom domain.

From many raw 2fold zoom images to one long strip.

A modified bump-mapping approach.

Subdivide only near the boundary.

Around embedded Julia sets in the Mandelbrot set.

Using Newton's method.

Fixing code from 1992.

Rebasing from a reference point.

Handwritten notes on various properties.

An xmas present for someone special.

Conformal mapping using Möbius transformations.

A series of approximations result in a simple formula.

Exploring external angles.

Structures in the hairs.

Some notes on various aspects of design and potential implementation.

another representation function

cutting and pasting binary digits of external angles

finding tuned branch points

speeding up external ray tracing

Mandelbrot Set explorer using OpenGL 4

26 images of the Mandelbrot Set

Following distance estimates.

Lots to think about.

Now hopefully more easily installable.