1. Dynamic cellular automata control using multiple recurrent neural nets and unsupervised learning

2. Background
“Structurally dynamic” cellular automata (Ilachinski, Halpern 1987) have been shown to simulate biological functions with emergent behavior
“Agent-based” models show how complex macro behavior in a population emerges from simple individual rules
My model is not structurally dynamic, just dynamic
I used neural nets because they allow for a broad search space of cellular behavior, given some fixed environmental challenges.

3. Cellular automata
Written in Typescript, a JavaScript superset with types
Uses JavaScript library of neuron nets, Synaptic.
Allows for arbitrary “projecting of layers”
Composable

4. Demo
Jamiesonwarner.com/plants

5. Setting The cellular automata is an M by N grid of cells.
Each cell is a “fluid vector” {f1, …, fn}, each fi is a scalar.
The “plant” is the set of living cells in the automata.
Some dynamic systems simulated: diffusion, osmosis, and biological functions: photosynthesis, active transport, cell metabolism, cell death, and cell reproduction

6. Control model
A set of m actions is defined. Each tick, every cell executes one of the m actions.
Each living cell is assigned a cell type
Each cell type x action pair is assigned a neural net:
n inputs, where n is the number of fluids
1 output, representing the decision weight for this action
Every tick, the decision weight for every action is computed on every cell, and the action chosen is result of the softmax function over the decision weights

7. Action directionality
I wanted action choices to be symmetric left and right
To accomplish this, whenever a “directional” action is performed,
First the fluid gradient is computed at the performing cell (2 x n-dimensional)
Then the direction computed is a constant matrix times the fluid gradient

8. Problem encountered: balancing
Some early environmental challenges made it “too hard” for plant growth.
For instance early plants would die of dehydration immediately upon reaching the air because the air had lower humidity levels => death by passive transport
As a solution I decreased passive transport into the plant, and gave plants the ability to regulate water pressure by pumping fluid from cell to cell.

9. Training Random search over all weights of the neural nets
(BIG search space)
Fitness is defined as the number of living cells after G=100 ticks

10. Extensions
Relax adjacency constraints to make a “structurally dynamic” cellular automata (Ilachinski, Halpern 1987)
Get rid of cell types in favor of finer control over the fluid vector
Every dimension of the fluid vector (past dimension K) gets its own neural net
The value fi , i >K, is the sum of its current value and the output of the neural net
Use simulated annealing search

11. Project url: https://github.com/jamiesonwarner/springfever