A collection of original interactive mathematical experiments and essays—all running live in your browser with no installation required. Each lab is a small piece of in-browser mathematical research, not a textbook visualization.
🔗 Live site: math.cognotik.com
Open index.html in any modern web browser, or serve the folder with any static file server:
npx serve .
# or
python -m http.serverThen navigate to the URL shown in your terminal (e.g. http://localhost:3000 for serve, http://localhost:8000 for
Python).
Extended interactive studies, each accompanied by documentation describing the underlying mathematics, motivation, and methods.
| Laboratory | Description |
|---|---|
| Pentagonal Lattice Geometry | Multi-sheeted covering construction where the pentagon develops fractional dimension (d ≈ 2.37) and spinor-like holonomy |
| Space-Color Symmetry | A pixel canvas where symmetry rewires the diffusion graph, producing kaleidoscope dynamics on a quotient-like manifold |
| Geometric Entropy | A continuous analogue of the Erdős distinct-distance problem via Shannon entropy optimization |
| Spacelike Knots | A knot equipped with a Minkowski metric, turning crossings into causal inversions |
| Layered Cellular Automata | Langton's ants write a colored substrate gating where Conway's Life can live — three feedback layers |
| Fractal Learning | Inverse iterated-function-system fitting via gradient optimization under a Chamfer metric |
| Irrational Lattice | Deterministic, algebraic "colored noise" for lattices — provably aperiodic, spectrally tunable |
Extended written investigations into the foundations of computational mathematics.
| Essay | Description |
|---|---|
| Quadratic Quasi-Newton | A new optimization algorithm interpolating between gradient descent and L-BFGS |
| Rational Certificate Complexity | A computational taxonomy of mathematical constants, stratified by certificate cost |
| The Simplest Increment: x + sin(x) | A cubic-convergent iteration for π built from the derivative structure of an analytic function |
| Numbers as Machines | A generator-based numerics library where every number is a deterministic, forkable virtual machine |
Compact, self-contained demonstrations of classical mathematical concepts.
| Demonstration | Description |
|---|---|
| Mandelbrot Set | Zoom and pan the iconic complex-plane fractal |
| Prime Number Sieve | Animated Sieve of Eratosthenes |
| Fourier Series | Build waveforms from rotating circles |
| Collatz Conjecture | Visualize the 3n+1 sequence |
index.html ← Landing page / experiment gallery
css/
style.css ← Shared stylesheet
home.css ← Landing page styles
js/
home.js ← Landing page logic (README previews, modals)
marked.min.js ← Markdown renderer
optimizer-*.js ← Shared QQN / Adam / L-BFGS optimizers
experiments/
basic/ ← Short classical demonstrations
Pentagon_Lattice_Geometry/ ← Multi-sheeted polygon covers
symmetry_simple/ ← Space-Color Symmetry
geometric-entropy/ ← Continuous Erdős distinct-distance
spacelike-knots/ ← Minkowski-metric knots
layered_ca/ ← Langton's ants × Conway's Life
fractal_learning/ ← Inverse IFS fitting
irrational_lattice/ ← Algebraic colored-noise lattices
essays/
QQN/ ← Quadratic Quasi-Newton
RCC/ ← Rational Certificate Complexity
PI_RCC/ ← The Simplest Increment: x + sin(x)
NAM/ ← Numbers as Machines
terraform/ ← Infrastructure for static hosting (S3 + CloudFront)
scripts/ ← Sitemap and OG-image generation
Implemented in plain HTML, CSS, and JavaScript — no build step, and no dependencies beyond a couple of CDN-loaded libraries (MathJax, Mermaid). Deployed as a static site to AWS S3 + CloudFront via Terraform.
See LICENSE.