Cellular Automata

Summary

In this post I explore Robert Bridson’s paper: Fast Poisson Disk Sampling in Arbitrary Dimensions and provide an example python implementation. Additionally, I introduce an alternative method using Cellular Automata to generate Poisson disk distributions.

Poisson disk sampling is a widely used technique in computer graphics, particularly for applications like rendering, texture generation, and particle simulation. Its appeal lies in producing sample distributions with “blue noise” characteristics—random yet evenly spaced, avoiding clustering.

Summary

This post is about color wars: a grid containing dynamic automata at war until one dominates.

Implementation

The implementation consists of two core components: the Grid and the CellularAutomaton.

1️⃣ CellularAutomaton Class

The CellularAutomaton class represents individual entities in the grid. Each automaton has:

• Attributes: ID, strength, age, position.
• Behavior: Updates itself by aging, reproducing, or dying based on simple rules.

2️⃣ Grid Class

The Grid manages a collection of automata. It:

Summary

The Nagel-Schreckenberg (NaSch) model is a traffic flow model which uses used cellular automata to simulate and predict traffic on roads.

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Design of the Nagel-Schreckenberg Model

1. Discrete Space and Time:

   • The road is divided into cells, each representing a fixed length (e.g., a few meters).
   • Time advances in discrete steps.

2. Vehicle Representation:

   • Each cell is either empty or occupied by a single vehicle.
   • Each vehicle has a velocity (an integer) which determines how many cells it moves in a single time step.

Rules of the Model:

• The NaSch model uses local rules to update the state of each vehicle at every time step. These rules are:

1. Acceleration:

Summary

I started with this paper A developmentally descriptive method forquantifying shape in gastropod shells and bridged the results to a cellular automata approach.

An example of the shell we are modelling:

Steps

1️⃣ Identify the Key Biological Features

The paper outlines the logarithmic helicospiral model for shell growth, where:

• The shell grows outward and upward in a spiral shape.
• Parameters like width growth (\(g_w\)), height growth (\(g_h\)), and aperture shape dictate the final form.

These features describe how the shell expands over time in a predictable geometric pattern.

Summary

This page is the first in a series of posts about Cellular Automata.

I believe that we could get the first evidence of AI through cellular automata.

A recent paper Intelligence at the Edge of Chaos found that LLM’s trained on more complex data generate better results. Which makes sense in a human context like the harder the material is I study the smarter I get. We need to find out why this is also the case with machines. The conjecture of this paper is that creating intelligence may require only exposure to complexity.