neural-cellular-automaton
where neural networks meet cellular automata in self-organizing computational structures
The Mathematics of Neural CA
Cell Neural Architecture
Each cell contains a feedforward neural network that processes neighbor states:
- • Input Layer: Receives neighbor cell activations
- • Hidden Layers: Process information through nonlinear transformations
- • Output Layer: Determines new cell state and signals
- • Weight Evolution: Synaptic plasticity based on local activity
Learning Rules
Hebbian Learning
Neurons that fire together wire together - strengthening correlated connections
Spike-Timing Dependent Plasticity
Temporal order of activation determines synaptic changes
Homeostatic Plasticity
Maintains stable activity levels through regulatory mechanisms
Evolutionary Selection
Networks compete and reproduce based on fitness criteria
Emergent Behaviors
Complex computational patterns emerge from simple rules:
- • Pattern Recognition: Networks learn to detect spatial configurations
- • Signal Propagation: Information waves through the cellular medium
- • Memory Formation: Stable attractor states store information
- • Computation Islands: Specialized regions for different tasks
- • Adaptive Response: Networks adjust to changing input patterns
References & Inspiration
- • Mordvintsev et al. - "Growing Neural Cellular Automata"
- • Randazzo et al. - "Self-classifying MNIST Digits"
- • Miller & Downing - "Evolution of Digital Organisms"
- • Wolfram - "A New Kind of Science"