Visualizing computation in large-scale cellular automata

Abstract

Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for enough computational capacity. Understanding complex computations happening in cellular automata and other systems capable of emergence poses many challenges, especially in large-scale systems. We propose methods for coarse-graining cellular automata based on frequency analysis of cell states, clustering and autoencoders. These innovative techniques facilitate the discovery of large-scale structure formation and complexity analysis in those systems. They emphasize interesting behaviors in elementary cellular automata while filtering out background patterns. Moreover, our methods reduce large 2D automata to smaller sizes and enable identifying systems that behave interestingly at multiple scales.

Self-Replication, Spontaneous Mutations, and Exponential Genetic Drift in Neural Cellular Automata

“…8 shows the results of using a "seed cloud" to code for different pattern. The scheme has some similarities with Cisneros et al (2022), except that all our seeds contain exactly the same genetic code. In consequence, the seeds initially develop identically, until they make contact with each other and the location of the contact serves to break the symmetry.…”

“…Yet most publications on NCA use a one-to-one mapping between automata and organisms: one organism is modeled by one automata, and if two organisms interact (for example through parasitism) each follows the rules of its own dedicated automaton. We know of 3 exceptions: Otte et al (2021), where a NCA is trained to in-paint several images from edges, Cavuoti et al (2022), where two set of rules are explicitly encoded in the model using hand-designed constraints; and Cisneros et al (2022) where several organisms are grown and hybridized. Note that these works are not about evolution and therefore do no not have self-replication mechanisms, but Cisneros et al (2022) in particular (while not being a traditional publication) shows interesting developmental modularity.…”

The Role of Evolution in Machine Intelligence

“…Other tools to assist in the scalable identification of these sorts of behaviors will be useful. These include producing summary visualizations [7], and filtering large state spaces for interesting structures [30].…”