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.
1. 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. 2. Grid Class The Grid manages a collection of automata.
Summary The Nagel-Schreckenberg (NaSch) model is a traffic flow model which uses used cellular automata to simulate and predict traffic on roads.
Design of the Nagel-Schreckenberg Model 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. 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.
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 1. 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.
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.