official website of the course: https://edu.epfl.ch/coursebook/en/cellular-automata-and-models-of-artificial-life-MATH-527
What is Artificial Life About?
The aim of ALife is to study the fundamental mechanisms of life while abstracting away from the particularities of its biological implementation. One key goal is to recreate such process in a computer simulation. The field is very diverse and interdisciplinary in its nature, and in this course we will focus on the theoretical results that can be presented with mathematical rigor. We will study dynamical systems, and the interplay between the notions of self-replication, computation, and dynamical properties in such systems. The most classical model we will cover in detail are cellular automata, which often produce fascinating visualizations from iterating very compact local rules. Below, I will give a quick overview of some ALife models with intriguing dynamics - it is likely you have already encountered some of them.1
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Game of Life
The most classic example of a cellular automaton in two-dimensions with two states.
Game of Life iterated from a random initial configuration.
Green shows a few past states to better see movement.
Game of Life construction: a ‘vacuum cleaner’.
Game of Life simulating another 2D cellular automaton.
High level.
Game of Life simulating another 2D cellular automaton.
Zoom-in.
Elementary Cellular Automaton Rule 110
A famous one-dimensional example of a cellular automaton with a very compact local rule which is Turing complete.
Rule 110 iterated from a random initial configuration.
Rule 110 simulating a cyclic tag system.
Barricelli’s model
One-dimensional version.
Two-dimensional version.
John von Neumann’s Universal Self-Replicator
Rules for constructing new states.
A pulser periodically emitting the sequence 10100.
The full construction.
Smaller Self-Replicators
Byl’s Loop.
Perrier-Sipper-Zahnd loop.
Evoloops.
Continuous Systems
Lenia with a single channel.
Lenia with RGB channels I.
Lenia with RGB channels II.
Lenia with RGB channels III.
Neural cellular automata.
Reaction-diffusion model.
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The figures with dark gray background were generated using the open-source software Golly, a cellular automaton simulator developed by Andrew Trevorrow and Tomas Rokicki. All the other figures were generated using PyCA, a Python library facilitating the implementation of artificial life models, developed by my colleague Vassilis Papadopoulos. ↩︎