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. These are decades of personal mathematical insight, finally carried to completion: AI-assisted tooling supplied the leverage to finish the exploration and publish it — but the questions, intuitions, and results are human.

“What happens if you poke a rigid structure with one irrational?”

Start Here

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 in a diffusion graph, a single causal direction in a knot — small perturbations that produce surprisingly rich behavior.

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 — fractional dimension, aperiodic moiré, spinor-like holonomy.
Dynamics on symmetric or causal substrates. Space-Color Symmetry and Layered CA wire symmetry orbits or substrate colors into the dynamics; the result is diffusion on a quotient manifold or three-layer feedback between agents and a Conway-Life host.
New metrics on familiar objects. Geometric Entropy recasts the Erdős distinct-distance problem as a continuous entropy optimization; Spacelike Knots equips a knot with a Minkowski metric so crossings become causal inversions.

If you only have a few minutes, open Pentagon Lattice Geometry or Spacelike Knots — they're the most self-contained, 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 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 do 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, motivation, and methods. Click a card to read its full notes; use the Open button to launch the lab.

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, not research — start here if you'd rather see something familiar.