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.

Structurally equivalent Latin squares

Canonicalization over symmetries allows them to be counted.

Rollover 2017

Another arbitrary counter rolls over, hooray.

Finding parents in the Farey tree

An application of the extended Euclidean algorithm.

Approximating cosine (update)

Claims of total superiority were premature.

Plastic rectangles

The non-trivial partitioning of a square into 3 similar rectangles.

Collatz fractal

Piecewise integer recurrence translated to complex function.

Complex squaring

Benchmarking three different implementations.

Simpler series approximation

When thinking a bit harder beats elaborate computer code.

Julia morphing symmetry

Rotation numbers in angled internal addresses are significant.

Floating point with extended exponent range

For when you need really big numbers without high precision.

Möbius Infinity

Square cross-section lemniscate of Bernoulli, with a twist.

Approximating cosine

9th order polynomial is both faster and more accurate than table lookup.

Biquad conversions

pole-zero -vs- direct form 2 -vs- pure-data

Modes on a plate

Solving sparse eigensystems with Octave.

Misiurewicz domains

An extension of atom domains to preperiodic points.

External angles of Misiurewicz points

Numerical investigations, hoping for a combinatorial revelation.

Clockpunch Theorems

Do the hands of clockpunch ever form a regular hexagon?

Stretching cusps

Conformal mapping using Möbius transformations.

Atom domain size estimation

A series of approximations result in a simple formula.


A cube of cubes that can be turned inside out.

Fish variations

Generalizing a tiling into hyperbolic variants.

Stroking curves of constant width

An approximation for relatively narrow widths.

Rectangles on a triangular lattice

always contain a multiple of 4 triangles