Executive summary
p2-odd-rays-visual-math-toy maps each positive integer by separating its power of two from its odd component. One view places successive ranges on square perimeters; another lays the same structure out as rays converging toward one. The Python generator exports SVG, PNG, and optional coordinate data. This is an archived visual and educational artifact. Its value is the construction and the images, not a theorem, cryptographic method, optimization, or systems claim.
Problem and context
Every positive integer has a unique decomposition into a power of two and an odd core. That simple fact produces nested families: multiplying by two advances to the next shell while retaining the same core. The project asks how those families look when placed on square boundaries or straightened into a ray diagram.
What was built
- A Python command-line generator for small labeled maps, odd-core rays, and
- A square-perimeter view using a bit-reversed integer order.
- A second view that places shells on vertical lines and exposes shared odd-core
- Retained SVG and PNG outputs with repository checksums.
- Historical CUDA and theta experiments separated from the main descriptive
coordinate inspection.
slopes.
visualization.
How it works
The exponent of two selects a shell and the odd core selects a ray. On the square view, a bit-reversal key orders positions around four edges. On the ray view, rational slopes align values with the same odd component. Floating point is used for rendering; the construction itself uses integer, rational, and bitwise operations.
Evidence and validation
The repository retains the script used to generate the published images and includes checksums for the committed outputs. The two layouts are alternative views of the same defined mapping, which makes individual coordinates inspectable. This is reproducibility of an illustration, not validation of an external mathematical claim.
Boundaries
The project is not peer-reviewed research and makes no claim of practical performance, cryptographic value, or deeper mathematical significance. Visual patterns are artifacts of the chosen construction. The repository is archived for transparency, including AI-assisted and failed experiments.
Repository map and first run
python3 demo.py small-map --exp 8 --with-rays
python3 demo.py odd-core-rays --exp 12
python3 demo.py ray-structure --exp 9The source README explains both mappings. pngs/ and the retained SVG files show the outputs, while failed_experiments/ and cuda/ are historical context rather than supported production paths.