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https://github.com/ratwolfzero/spacetime

Quantum Golomb Spacetime Simulator
https://github.com/ratwolfzero/spacetime

emergent emergent-behavior golomb golomb-ruler quantum-mechanics spacetime

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Quantum Golomb Spacetime Simulator

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README 

          
# 🧠 Quantum Golomb Spacetime Simulator



> ## *My Spacetime is Made of Numbers and Poor Decisions*  

>

> ### *Inside the Quantum Golomb Simulator That Accidentally Discovered the Universe*



![Quantum Golomb Spacetime](Quantum_Golomb_Spacetime_Analysis.png)



> *“Some say the universe began with a bang. This one began with `[0, 1]` and a poorly tuned random number generator.”*



---



## 📌 Overview



This project simulates a playful model of spacetime growth inspired by:



- 🧮 **Golomb rulers**

- 🎲 **Quantum fluctuations**

- 🌌 **Curved geometry**

- 🕸 **Causal networks**



While not physically rigorous, the simulator explores how *structure, density, and curvature* can emerge from simple number-theoretic rules—rendered with surprisingly rich visualizations.



---



## 📐 What Is a Quantum Golomb Spacetime?



A **Golomb ruler** is a set of integers (marks) such that all pairwise distances are unique.



In this simulator:



- Each mark is treated as a **discrete event** in time.

- New marks are added via a **temperature-driven growth process**.

- A synthetic **matter–curvature interaction** perturbs new candidates.

- The result is embedded in **polar coordinates**, giving rise to:

  - Mass density fields

  - Local curvature

  - Causal structure

  - Fractal geometry



> ⚠️ This is not quantum gravity—just quantum creativity.



---



## 🌱 Step 1: Birth of the Universe



We begin with two marks:



```python

simulator = QuantumGolombSpacetime(initial_marks=[0, 1])

simulator.quantum_growth(max_marks=40, temperature=0.1)

````



Growth proceeds by probabilistically selecting the next valid integer that maintains the Golomb condition (no repeated distances). The `temperature` parameter controls how chaotic the search is:



- **Low T** → Conservative, stable expansion

- **High T** → Chaotic, entropy-maximizing behavior



---



## 🔀 Step 2: Quantum Decisions (and Other Mistakes)



The system's growth isn't deterministic — it's guided by temperature-controlled randomness.

Low temperatures yield precise, deliberate mark choices; high temperatures allow chaotic, exploratory additions.

Starting from the third mark onward, growth becomes influenced by an emergent interaction:



$$

\text{Potential} \sim \sum_i \frac{\rho_i}{d_i^2 + \varepsilon}

$$



Where:



- \$\rho\_i\$ = local matter density

- \$d\_i\$ = distance to existing mark \$i\$



This interaction biases the selection of new candidates, introducing asymmetry and reinforcing local structure.

Though **curvature** is formally introduced in Step 3, this effect lays the groundwork — subtly shaping how space (and regret) unfold.



---



## 🌀 Step 3: Polar Embedding



Each mark is mapped into 2D using polar coordinates:



$$

x = r \cdot \cos(\theta), \quad y = r \cdot \sin(\theta)

$$



Where:



- \$r\$ = log-scaled radial distance from origin

- \$\theta\$ = angular position around the circle (uniform spacing)



This creates a spiraling spacetime diagram that reveals geometric clustering and local tension.



---



## 🌌 Step 4: Mass Density and Fractal Geometry



The polar embedding is converted into a 2D density map using Gaussian-smoothed binning. We then estimate the **fractal dimension** using box-counting:



$$

D = \lim_{\varepsilon \to 0} \frac{\log N(\varepsilon)}{\log(1/\varepsilon)}

$$



> Example result: `Estimated fractal dimension: 2.181`



This value suggests dimensional emergence or compactified structure.



---



## 🔊 Step 5: FFT of the Density Field



We apply a 2D Fast Fourier Transform (FFT) to the mass density map. This reveals:



- Radial and angular **symmetries**

- Hidden **periodicities**

- Noise or self-similarity signatures



---



## 🧭 Step 6: Causal Network Construction



We build a causal graph where:



- **Nodes** = Events (marks)

- **Edges** = Future-directed links based on angular proximity

- **Weights** encode difficulty of information transfer:



$$

w_{ij} = \frac{\rho_i}{\Delta t_{ij} \cdot (\Delta\theta_{ij} + \delta)}

$$



The graph reflects how events influence each other, with metrics like:



- Causal connection density

- Average path length

- Degree–matter correlation



---



## 📊 Diagnostics: Quantum Physics with a Wink



### 🧬 Quantum Fluctuations



Average deviation from uniform growth is computed as:



```python

Quantum Fluctuation = mean(abs(∆position - 1))

```



Captures jitter introduced by temperature and curvature feedback.



---



### 🌐 Curvature–Matter Feedback



We compute **local curvature** from nearest-neighbor triangles. Higher curvature regions receive more "matter"—mimicking attraction.



---



### ⚖️ Energy Balance (Kind Of)



A toy-model energy proxy is defined as:



$$

\text{Energy} \sim \frac{\text{Total Matter}}{\text{Average Curvature}}

$$



This ratio is tracked across growth to observe pseudo-conservation behavior.



---



## 📈 Visualization Dashboard



The simulator outputs a 6-panel visual summary:



| Panel | Content Description      |

| ----- | ------------------------ |

| 📍    | Polar Embedding (r, θ)   |

| 🌋    | Smoothed Mass Density    |

| 🔊    | FFT of Density Field     |

| 🪐    | Local Curvature Map      |

| 🌐    | Causal Network Diagram   |

| 🌈    | Matter Density per Event |



All panels include colorbars and standardized axis ratios for interpretability.



---



## 🧠 Summary of Findings



While this simulation is fictional and symbolic, it provides:



- A **sandbox for emergent structure** from simple constraints

- A new way to look at **Golomb uniqueness as causal order**

- Feedback loops between **matter, curvature, and event layout**

- Visual metaphors for **dimensional compactification**, **causal flow**, and **quantum foam**



---



## 💡 Philosophical Addendum



> “My universe grew, curved, pulsed, and linked. All from `[0, 1]`.

> Just like ours—chaotic, kind of pretty, and mostly made up.”



You may not find a Theory of Everything, but you might:



- Build intuition for emergent geometry

- Appreciate discrete structures as creative fuel

- Laugh at causality’s LinkedIn behavior



---



## 🛠 Requirements



```bash

pip install numpy matplotlib scipy scikit-learn networkx scikit-image

```



---



## ⚠️ Note



This simulator is designed for **exploration and metaphor**, not physical accuracy.

But it might replace your existential dread with constructive curiosity.  



Note on Computational Artifacts



While some features may stem from numerical artifacts or boundary effects, the central insight holds: complexity and geometry can emerge from minimalist, rule-based logic. This model isn’t a literal blueprint of spacetime — but it consistently produces structured behavior from simple combinatorial constraints, making it a valuable tool for intuition and exploration



Note on Golomb search limit:  



All visualizations shown here use a Golomb search limit of 1000. Pushing this limit to 10,000 alters the growth dynamics and dimensional scaling.



---



## 🧠 Quick Summary: Physics Behind the Simulator



> See full annex: [ANNEX\_PhysicsBehindTheSimulator.md](./ANNEX_PhysicsBehindTheSimulator.md)



1. **Golomb Rulers = Distinct Quantum Events**

   Unique distances prevent overlap — like enforcing unitarity in quantum systems.



2. **Thermal Growth = Quantum Fluctuations**

   Randomized mark addition simulates vacuum noise or inflation-like expansion.



3. **Matter Density = Mass-Energy Field**

   Each mark contributes to a local scalar field influencing future growth.



4. **Numeric Potential = Proto-Curvature**

   Attraction toward denser regions mimics curvature before geometry exists.



5. **Polar Embedding = Emergent Geometry**

   Spatial coordinates are constructed, revealing extrinsic curvature and structure.



6. **Fractal Dimension = Spacetime Texture**

   Dimension $D$ evolves from chaotic >2.0 to smooth \~2.0, reflecting emergence.



7. **Causal Network = Information Flow**

   Directed edges encode relativistic causal relations between events.



8. **Spectral FFT = Hidden Structure**

   Fourier analysis of matter density reveals holographic/spectral patterns.



9. **Curvature vs. Matter = Balance Law**

   A toy energy-like quantity $E = \rho / \langle K \rangle$ remains approximately stable.



10. **Dimensional Emergence**

    Early universe is foamy and noisy; later universe becomes geometric and causal.