Mathematical Explorations
A collection of original interactive mathematical experiments and essays running live in the browser — each lab a small piece of in-browser mathematical research, not a textbook visualization. Labs include Pentagonal Lattice Geometry, Space-Color Symmetry, Geometric Entropy, Spacelike Knots, Fractal Learning, and more. Claims verified computationally via Maxima, BFS sweeps, and KPM estimation.
Key Features
Original Mathematical Research
Research-grade constructions including Pentagonal Lattice Geometry (fractional dimension, spinor-like holonomy), Geometric Entropy (continuous analogue of Erdős distinct-distance problem), and Spacelike Knots (Minkowski-metric knots).
- Pentagonal Lattice Geometry with fractional dimension
- Geometric Entropy: continuous Erdős distinct-distance analogue
- Spacelike Knots in Minkowski metric
- Fractal Learning: inverse IFS fitting via gradient optimization
Computationally Verified Claims
Symbolic identities verified via Maxima batch scripts; spectral behavior confirmed via BFS dimension sweeps and KPM estimation.
- Maxima batch scripts for symbolic verification
- BFS dimension sweeps for spectral confirmation
- KPM estimation for independent validation
- Reproducible in-browser experiments
Zero Build Step Deployment
Plain HTML, CSS, and JavaScript with no build step, deployed as a static site to AWS S3 + CloudFront via Terraform.
- No framework, no bundler, no build step
- AWS S3 + CloudFront via Terraform
- Instant load, works offline
- Accompanied by formal essays (QQN, Rational Certificate Complexity, Numbers as Machines)
Getting Started
No installation required! Visit the live site:
https://math.cognotik.com/
All experiments run directly in your browser.
Quick Example
Featured Labs
- Pentagonal Lattice Geometry — fractional dimension, spinor-like holonomy
- Geometric Entropy — continuous analogue of the Erdős distinct-distance problem
- Spacelike Knots — knot theory in Minkowski metric
- Fractal Learning — inverse IFS fitting via gradient optimization
- Layered Cellular Automata — multi-layer CA dynamics
- Irrational Lattice — lattice geometry with irrational bases
Classic Demos
- Mandelbrot set explorer
- Prime sieve visualization
- Fourier series decomposition
- Collatz conjecture paths
Formal Essays
- Quadratic Quasi-Newton
- Rational Certificate Complexity
- Numbers as Machines
Technical Details
Technologies
Requirements
- Modern web browser with JavaScript enabled
- No installation or account required
Contribute to the Project
This is an open-source project. Contributions, bug reports, and feature requests are welcome from the community.