Local Governor Photon Billiard Simulation

A computational investigation of proximity-based governance in photon billiard systems. Each universe (container) has a single governing body at its center that only affects photons when they come close — creating a natural Goldilocks zone where photons must dance around the governor: close enough to feed, far enough to survive.

Architecture

The Governor

A central governing body with a numerical value (7, 13, 42, 100, 333, 999) that sits at the origin of each universe. It has:

• Interaction radius: 5.0 units — photons within this range are affected
• Proximity threshold: 2.0 units — photons within this range receive maximum effect
• Energy field: absorbs/emits energy to photons based on proximity
• Digit extraction: extracts the thousandths digit from distance / governor_value to determine photon size class

Photons

Extremely small particles (radius ~0.001) that:

• Start on a ring 3.0 units from the governor with tangential velocity
• Move at high speed (5-15 units per step)
• Absorb energy from the governor when close (growing in size)
• Can spawn new photons when they grow too large (radius > 0.12)
• Can be eliminated if they absorb too much energy (KE > 50)
• Get repelled if they get too close to the governor (< 0.6 units)

Simulation Mechanics

• Micro-steps: Each macro-step = 5 micro-steps, allowing photons to pass through the interaction zone
• Container walls: Only checked at macro-step boundaries
• Governor interaction: Happens during every micro-step when photons are in range

Containers (Universes)

Container	Geometry	Behavior
Sphere	r=10	Photons orbit freely, strong interaction, cascading spawning
Cube	s=20	Photons bounce off walls, rarely reach center, minimal interaction
Ellipsoid	a=15,b=10,c=8	Moderate interaction, some spawning, no deaths
Sinai	s=20, obs=4	Chaotic obstacle pulls photons inward, total extinction
Cylinder	r=10,h=20	Moderate interaction, stable spawning ecosystem

Results

Energy Production (Total Energy at Step 2000)

Container	Best Governor	Total Energy	Change	Survivors
Sphere	333	536.01	+751%	38/40
Sphere	100	470.14	+671%	23/26
Sphere	999	427.33	+619%	20/22
Sphere	42	375.88	+556%	15/18
Sphere	7	241.80	+394%	24/27
Ellipsoid	333	-1.44	+98%	9/9
Ellipsoid	999	-2.68	+97%	10/10
Cylinder	999	-64.70	+21%	8/8
Cube	7	-74.29	+10%	3/3
Sinai	Any	0.00	100%	0/3

Key Findings

1. Sphere (G=333) wins — 536 total energy, +751% growth, 38/40 photons survived. The sphere allows photons to orbit freely and interact with the governor repeatedly, creating cascading spawning.

2. Sinai is a death trap — 0% survival across all governors. The chaotic circular obstacle deflects photons toward the center where they absorb too much energy and are eliminated.

3. Cube is stable but dead — 100% survival, but only +10% energy growth. Photons bounce off walls and rarely reach the interaction zone.

4. Governor 333 is optimal — highest energy across all containers that survive, most spawns (37 in sphere), fewest deaths (2). The digit extraction from distance/333 creates rich variation in photon sizes.

5. Digit diversity matters — Governor 333 divides distance by 333, producing varied thousandths digits (0-9) that create diverse photon sizes. Governor 7 divides by 7, producing coarser digit resolution that leads to uniform sizes and eventual elimination.

6. Goldilocks containers — Ellipsoid and cylinder provide moderate interaction: some spawning, no deaths, slow but steady energy growth.

The Goldilocks Principle

The system demonstrates a fundamental Goldilocks principle:

• Too chaotic (Sinai): photons pulled into governor → death
• Too stable (Cube): photons never reach governor → stagnation
• Just right (Sphere): photons orbit, feed, spawn, survive → exponential growth
• Moderate (Ellipsoid, Cylinder): limited interaction, slow growth, high survival

Files

• local_governor_simulation.py — Main simulation code
• create_local_governor_figures.py — Figure generation
• local_governor_results.json — Full simulation results
• figures/ — Publication-quality figures

Figures

1. fig1-energy-heatmap.png — Energy production heatmap across containers and governors
2. fig2-energy-growth.png — Energy growth percentage and spawn events
3. fig3-energy-timelines.png — Energy, survival, and proximity timelines
4. fig4-survival.png — Survival rates and elimination analysis
5. fig5-concept-diagram.png — Visual overview of each container's dynamics

Mathematical Foundation

Digit Extraction

digit = floor(|distance / governor_value| × 1000) mod 10

This creates a discrete size class (0-9) from continuous distance, encoding the continuous billiard dynamics into a discrete computational layer.

Proximity Factor

pf = ((interaction_radius - dist) / (interaction_radius - proximity_threshold))²

Quadratic falloff from 1.0 at proximity threshold to 0.0 at interaction radius.

Energy Absorption

energy_absorbed = pf × absorption_rate × speed × 0.02

Proportional to proximity, speed, and governor absorption rate.

Size Growth

new_radius = (0.001 + digit × 0.001) + energy_absorbed × 0.05 + growth_steps × 0.0005

Base size from digit + energy contribution + cumulative growth.

Reproducing Results

python3 local_governor_simulation.py
python3 create_local_governor_figures.py

Citation

@misc{photon_billiard_local_governor,
  title = {Local Governor Photon Billiard Simulation},
  author = {Alex},
  year = {2025},
  url = {https://github.com/alexsysctrl/local-governor-photon-billiard}
}

License

MIT