Boolean Tile Basis
From truth tables to Ising Hamiltonians — the complete 16-tile system
The full manuscript tracing the 16 Boolean tiles through Łukasiewicz logic, IFS fractals, Bloch-sphere quantum states, 2-qubit unitary gates, and Ising spin Hamiltonians (1649 lines, in-browser HTML).
Interactive Visualizations
2D annular-arc visualization of the IFS attractors. Each tile maps a 2D grid to concentric annular arcs with greyscale = accumulator value. Depth slider included. 2D IFS Chaos Game
3D spherical visualization of the 16 tiles using Three.js. Each tile's IFS accumulator maps to spherical coordinates: θ from row, φ from column, radius R = accumulator value. OrbitControls, auto-rotate, synchronized cross-tile camera. 3D Three.js Bloch
Supplementary Material
Chaos game rendered directly on the sphere surface.
Fractal Shepard tone — auditory representation of the IFS depth process.
An exposition of the many-worlds interpretation of the IFS depth process.
References
- Grim, P., Mar, G., & St. Denis, P. (1998). The Philosophical Computer: Exploratory Essays in Philosophical Computer Modeling. MIT Press.
- Grim, P. (1993). "Self-Reference and Chaos in Fuzzy Logic." IEEE Trans. Fuzzy Systems, 1(4), 237–253.
- St. Denis, P., & Grim, P. (1997). "Fractal Images of Formal Systems." Journal of Philosophical Logic, 26, 181–222.