CAX is a high-performance cellular automata library built on top of JAX/Flax that is designed for flexiblity.

CAX is a cutting-edge library designed to implement and accelerate various types of cellular automata using the JAX framework. Whether you're a researcher, a hobbyist, or just curious about the fascinating world of emergent and self-organizing systems, CAX has got you covered! 🧬

Despite their conceptual simplicity, cellular automata often demand significant computational resources. The parallel update of numerous cells, coupled with the need for backpropagation through time in neural cellular automata training, can render these models computationally intensive. CAX leverages hardware accelerators and massive parallelization to run cellular automata experiments in minutes. 🚀

The library works with discrete or continuous cellular automata of any spatial dimension, offering exceptional flexibility. From simulating one-dimensional elementary cellular automata to training three-dimensional self-autoencoding neural cellular automata, and even creating beautiful Lenia simulations, CAX provides a versatile platform for exploring the rich world of self-organizing systems.

Cellular Automata	Reference	Example
Elementary Cellular Automata	Wolfram, Stephen (2002)
Conway's Game of Life	Gardner, Martin (1970)
Lenia	Chan, Bert Wang-Chak (2020)
Growing Neural Cellular Automata	Mordvintsev, et al. (2020)
Growing Conditional Neural Cellular Automata	Sudhakaran et al. (2020)
Growing Unsupervised Neural Cellular Automata	Palm et al. (2021)
Self-classifying MNIST Digits	Randazzo, et al. (2020)
Diffusing Neural Cellular Automata	Faldor, et al. (2024)
Self-autoencoding MNIST Digits	Faldor, et al. (2024)
1D-ARC Neural Cellular Automata	Faldor, et al. (2024)

You will need Python 3.10 or later, and a working JAX installation.

Then, install CAX from PyPi:

pip install cax

To upgrade to the latest version of CAX, you can use:

pip install --upgrade git+https://github.com/maxencefaldor/cax.git

import jax
from cax.core.ca import CA
from cax.core.perceive.conv_perceive import ConvPerceive
from cax.core.update.nca_update import NCAUpdate
from flax import nnx

seed = 0

channel_size = 16
num_kernels = 3
hidden_layer_sizes = (128,)
cell_dropout_rate = 0.5

key = jax.random.key(seed)
rngs = nnx.Rngs(seed)

perceive = ConvPerceive(
	channel_size=channel_size,
	perception_size=num_kernels * channel_size,
	rngs=rngs,
	feature_group_count=channel_size,
)
update = NCAUpdate(
	channel_size=channel_size,
	perception_size=num_kernels * channel_size,
	hidden_layer_sizes=hidden_layer_sizes,
	rngs=rngs,
	cell_dropout_rate=cell_dropout_rate,
)
ca = CA(perceive, update)

state = jax.random.normal(key, (64, 64, channel_size))
state = ca(state, num_steps=128)

@misc{cax2024,
	title = {{CAX}: {Cellular} {Automata} {Accelerated} in {JAX}},
	url = {https://arxiv.org/abs/2410.02651},
	journal = {arXiv.org},
	author = {Faldor, Maxence and Cully, Antoine},
	year = {2024},
}