CAX: Cellular Automata Accelerated in JAX

CAX is a high-performance and flexible open-source library designed to accelerate artificial life research — cellular automata, particle systems, and other self-organizing complex systems, all in JAX. 🧬

Overview 🔎

Are you interested in emergence, self-organization, or open-endedness? Whether you're a researcher or just curious about the fascinating world of artificial life, CAX is your digital lab! 🔬

Designed for speed and flexibility, CAX allows you to easily experiment with self-organizing behaviors and emergent phenomena. 🧑‍🔬

Get started here

Why CAX? 💡

CAX supports discrete and continuous systems, including neural cellular automata, across any number of dimensions. Beyond traditional cellular automata, it also handles particle systems and more, all unified under a single, intuitive API.

Rich 🎨

CAX provides a comprehensive collection of 25+ ready-to-use systems. From simulating one-dimensional elementary cellular automata to training three-dimensional self-autoencoding neural cellular automata, or even creating beautiful Lenia simulations, CAX provides a versatile platform for exploring the rich world of self-organizing systems.

Flexible 🧩

CAX makes it easy to extend existing systems or build custom ones from scratch for endless experimentation and discovery. Design your own experiments to probe the boundaries of artificial open-ended evolution and emergent complexity.

Fast 🚀

CAX is built on top of the JAX/Flax ecosystem for speed and scalability. The library benefits from vectorization and parallelization on various hardware accelerators such as CPU, GPU, and TPU. This allows you to scale your experiments from small prototypes to massive simulations with minimal code changes.

Tested & Documented 📚

The library is thoroughly tested and documented with numerous examples to get you started! Our comprehensive guides walk you through everything from basic cellular automata to advanced neural implementations.

Examples 📓

#	Example	Reference
1	Elementary Cellular Automata	Wolfram (2002)
2	Conway's Game of Life	Gardner (1970)
3	Langton's Ant	Langton (1986)
4	Abelian Sandpile	Bak et al. (1987)
5	Lenia	Chan (2020)
6	Flow Lenia	Plantec et al. (2022)
7	Particle Lenia	Mordvintsev et al. (2022)
8	Reaction-Diffusion	Gray & Scott (1984)
9	Particle Life	Mohr (2018)
10	Boids	Reynolds (1987)
11	Neural Particle Automata	Kim et al. (2026)
12	Growing Neural Cellular Automata	Mordvintsev et al. (2020)
13	Growing Conditional NCA	Sudhakaran et al. (2022)
14	Growing Unsupervised NCA	Palm et al. (2021)
15	Diffusing Neural Cellular Automata	Faldor et al. (2024)
16	Self-classifying MNIST Digits	Randazzo et al. (2020)
17	Self-autoencoding MNIST Digits	Faldor et al. (2024)
18	Texture Neural Cellular Automata	Niklasson et al. (2021)
19	1D-ARC Neural Cellular Automata	Faldor et al. (2024)
20	Attention-based Neural Cellular Automata	Tesfaldet et al. (2022)
21	Isotropic Neural Cellular Automata	Mordvintsev et al. (2022)
22	Differentiable Logic Cellular Automata	Miotti et al. (2025)
23	Variational Autoencoder	Kingma & Welling (2013)
24	Recurrent Residual CNN	Faldor et al. (2024)
25	Growing NCA with Evolution Strategies	Faldor et al. (2024)
26	Growing NCA with Reinforcement Learning	Faldor et al. (2024)
27	Leniabreeder	Faldor & Cully (2024)
28	Gradient Descent in Lenia	Hamon et al. (2024)
29	Lenia Gradients in Depth	Faldor et al. (2024)

Getting Started 🚦

Here, you can see the basic CAX API usage with Conway's Game of Life:

import jax
import jax.numpy as jnp

from cax.cs.life import Life

seed = 0

num_steps = 128
spatial_dims = (32, 32)
channel_size = 1
rule_golly = "B3/S23"  # Conway's Game of Life

key = jax.random.key(seed)

birth, survival = Life.birth_survival_from_string(rule_golly)
cs = Life(birth=birth, survival=survival)

state_init = jax.random.bernoulli(
    key, p=0.5, shape=(*spatial_dims, channel_size)
).astype(jnp.float32)
state_final, states = cs(state_init, num_steps=num_steps, return_states=True)

For a more detailed overview, get started with this notebook

Installation ⚙️

You will need Python 3.12 or later, and a working JAX installation installed in a virtual environment.

Then, install CAX from PyPi with uv:

uv pip install cax

or with pip:

pip install cax

Citing CAX 📝

If you use CAX in your research, please cite the following paper:

@inproceedings{cax,
    title = {{CAX}: {Cellular} {Automata} {Accelerated} in {JAX}},
    volume = {2025},
    url = {https://proceedings.iclr.cc/paper_files/paper/2025/file/19206a6ed5ed0aaeed440448dfc5cf7e-Paper-Conference.pdf},
    booktitle = {International {Conference} on {Representation} {Learning}},
    author = {Faldor, Maxence and Cully, Antoine},
    editor = {Yue, Y. and Garg, A. and Peng, N. and Sha, F. and Yu, R.},
    year = {2025},
    pages = {8947--8960},
    keywords = {artificial life, emergence, self-organization, open-endedness, cellular automata, neural cellular automata},
}

Contributing 👷

Contributions are welcome! If you find a bug or are missing your favorite self-organizing system, please open an issue or submit a pull request following our contribution guidelines 🤗.