math ⇄ art lab

math art lab

Irrational digits, honeycomb lattices, factorization records — rendered as interactive art you can export as a background-image for any website. Base 12 is our native tongue: 0–9 ↊ ↋, dek & el.

experiment 01

Honeycomb Lab

π in any base on hex or square grids. One gradient per digit — now with your own colours & shades, digit shapes, a prime lens (Ulam on any path), a fraction garden (hue = denominator, shade = value), sequence search and image mapping. Stack the loops until interference patterns emerge — then take it home as CSS.

experiment 02

Dozenal Bestiary

π, e, φ, √2, √3, ln 2 — six irrationals, six honeycombs, side by side. Compare their digit fingerprints.

experiment 03

The RSA Room

RSA-250 = p × q, verified live in your browser in milliseconds — the computation that took 2,700 core-years to invert, drawn as a lattice heat map. Plus RSA-260, revealed Sep 3 2026.

experiment 04

The Toy Shelf

Modular times-table circles (cardioid machine), the Ulam spiral, and digit walks on the honeycomb lattice.

experiment 05

Fractal Conservatory

Mandelbrot, Julia, Burning Ship and Newton basins you can dive into — plus a real-time raymarched 3D Mandelbulb in raw WebGL, and a chaos game driven by π's digits instead of randomness.

experiment 06

The Key Forge

Forge your own RSA keys in-browser — Miller-Rabin primes in BigInt, textbook and OAEP encryption, PSS signatures — then render your modulus as art. Your protocol, your keys, nothing leaves the page.

Idea board — what to build next

🌀 Collatz coral — orbit lengths as branch angles
🎚️ Fourier epicycles tracing π's digits
🦋 Lorenz attractor in 3D (WebGL)
◐ Cyclic-number art — 1/7, 1/512… coloured by denominator
📐 Pascal's triangle mod 12 → dozenal Sierpiński
🎮 Game of Life on a hex grid, seeded by digits
🔊 Sonification — digit walks as melody (Web Audio)
🌀 Apollonian gasket & Kleinian limit sets
🌱 L-systems — dragon curves & plant grammars
🐎 Prime race — π(x) vs li(x) as two runners
✨ Diffusion-limited aggregation on the honeycomb
🎯 Normality meter — do the digits behave?

full backlog with sketches in IDEAS.md — pick one and it grows into a page.

Repos worth an afternoon

93.2k ★

3b1b/manim the one you asked for

Grant Sanderson's animation engine for explanatory math videos — the code behind every 3Blue1Brown animation. Python + OpenGL, MIT licensed. Install with pip install manimgl; all video source lives in the companion 3b1b/videos repo. The friendlier fork is ManimCommunity/manim.

535 ★

marcusvolz/mathart

Mathematical art with R: harmonographs, Lissajous curves & their k-nearest-neighbour graphs, mollusc shell models, the Lorenz attractor, fractal ferns, rapidly-exploring random trees.

curated

terkelg/awesome-creative-coding

The big list: creative-coding frameworks, shader platforms, generative-art tutorials — the map of this territory.

canonical

processing/p5.js · d3/d3 · Shadertoy

The workhorses: p5.js (Processing's JS sister — the Coding Train's tool), d3 for data-driven documents, Shadertoy for fragment-shader math art (see Inigo Quilez's articles).

factored

CADO-NFS

The open-source Number Field Sieve that cracked RSA-250 in 2020 — mathematics as heavy machinery. The RSA numbers list tracks the frontier.

Kin: the planet orbit visualiser

A small homage to the qalarc logo's planet orbit visualiser.

Same family as everything here: a few simple rules — orbit radii in geometric progression, constant angular speeds — iterated until resonance appears. Every experiment in this lab is that idea wearing a different coat: digits instead of planets, honeycombs instead of orbits.

This one runs three bodies with commensurable periods; watch them braid, align, and drift apart.