Interactive experiments · runs entirely in the browser

Mathematical Explorations

A collection of original interactive experiments in geometry, number theory, and dynamical systems; each lab is a small piece of in-browser mathematical research, not a textbook visualization. Most began as questions I'd carried for years — sometimes decades — that simply never had the tooling to be finished and shared. AI-assisted tooling supplied the leverage to close the loops and publish; the questions, the intuitions, and the results are human.

“What happens when you poke a rigid structure with a single irrational?”

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Most of the labs below share a single recurring question: what happens to a clean algebraic or geometric structure when you introduce one carefully chosen twist? A single irrational coordinate; a single symmetry edge wired into a diffusion graph; a single causal direction imposed on a knot. It turns out that these small, deliberate perturbations produce surprisingly rich behavior — and that watching the behavior emerge is often more instructive than the answer itself.

Three loose themes run through the featured labs:

Algebraic structure → emergent geometry. Pentagon Lattice and Irrational Lattice both start with a number field and watch geometry crystallize out of it; the field you put in — not the picture — turns out to be the real invariant, yielding fractional dimension, aperiodic moiré, and spinor-like holonomy.
Dynamics on symmetric or causal substrates. Space-Color Symmetry and Layered CA wire symmetry orbits or substrate colors directly into the dynamics; the result is diffusion that flows along a quotient manifold, or a three-layer feedback loop between crawling agents and a Conway-Life host.
New metrics on familiar objects. Geometric Entropy recasts the classical Erdős distinct-distance problem as a continuous entropy optimization; Spacelike Knots equips a knot with a Minkowski metric, so that every crossing becomes a causal inversion.

If you only have a few minutes, open Pentagon Lattice Geometry or Spacelike Knots; they're the most self-contained, the most novel, and the easiest to play with cold.

A note on provenance: none of this is generated insight. Each lab grew from a question I'd carried for years — sometimes decades — that simply never had the tooling to be finished and shared at a level of effort that made sense. AI-assisted exploration provided that leverage; it helped close the loops, build the visualizations, and handle the publishing. The mathematics, the intuitions, and the judgment about what was worth chasing are mine.

Extended interactive studies, each accompanied by documentation describing the underlying mathematics, the motivation, and the methods. Click a card to read its full notes; use the Open button to launch the lab and play with it yourself.

Playable sister projects and game-like labs, built on the same browser-native tooling as the experiments above. Click a card to read its notes; use the Open button to launch the game.

Extended written investigations into the foundations of computational mathematics. The RCC · PI_RCC · NAM trilogy forms a single arc — three angles on one question: what is a mathematical constant, computationally? Each treats a number not as a static value but as an engine whose structure, cost, and reachability can be measured. Click a card to read inline; use Open for the dedicated view.

Compact, self-contained demonstrations of classical mathematical concepts. These are warm-ups rather than research; start here if you'd rather see a familiar face before the deeper labs.