convoca

Demonstrate and learn cellular automata using convolutional neural networks in TensorFlow

The video above shows different stages of training a network to learn Conway's Game of Life. This code both implements and analyzes known CA rulesets using TensorFlow, and it also learns the rules of unknown CA given an image sequence as training data. If you find this code useful, please consider citing the accompanying publication:

Gilpin, William. "Cellular automata as convolutional neural networks." Physical Review E 100.3 (2019): 032402. arXiv

Demos and features

The demos.ipynb illustrates a minimal example of training a CNN on the Game of Life, including example outputs. Models are instantiated using the initialize_model(...) function, which builds a network with a trainable convolutional filter as the first layer, which serves to extract information about the neighborhood of each cell. Repeated 1x1 convolutions in subsequent layers implement the CA rules, and a final softmax layer assigns an output state to each cell. For cases in which the CA ruleset is radially symmetric, the optional SymmetricConvolution layer imposes radially-symmetric structure on the learned convolutional kernels, which is often the case for natural systems with "totalistic" rules. An optional Wraparound2D layer also allows periodic boundary conditions to be implemented in the convolutions.

Installation and Requirements

Install directly from GitHub using

pip install git+git://github.com/williamgilpin/convoca

Typical installation with Miniconda. This code has been tested on macOS and Ubuntu.

• Python >3.4
• TensorFlow >2.0
• numpy
• matplotlib
• Jupyter notebooks (for demos)

Structure

The package contains the following libraries

train_ca : requires TensorFlow

ca_funcs : requires TensorFlow

utils : minor functions that support the main methods. Requires numpy only.

demos.ipynb : demonstration of the code for learning the game of live

Updates

As of 2.26.2020, the code has been significantly re-factored to use Tensorflow 2.0 and Keras. The previous implementation has been placed in the "resources" directory, for reference.

Planned future work

• Add methods for simulating totalistic CA
• Add methods for Moore neighborhood CA
• Add demos recreating classic experiments, such as the results in Langton. Physica D, 1990.
• Add statistical physics calculations such as an efficient calculation of "activity" for a CA
• CA on graphs using an adjacency matrix --> grid convolutional operator