Orphans in Cellular Automata - December 2024

Explore a comprehensive Russian-language seminar lecture with English slides examining the fascinating world of cellular automata and Garden-of-Eden configurations. Delve into the mathematical concepts of non-surjective cellular automata, focusing on the characterization of configurations that lack preimages in system evolution. Learn about the duality between Garden-of-Eden configurations and orphans in finite patterns, and discover how these patterns can be identified using regular languages and finite-state machines. Examine the construction of de Brujin graphs for one-dimensional cellular automata, understanding their role in pattern recognition and system analysis. Study practical applications including the proof that every 1*n configuration of live and dead cells can appear in Conway's Game of Life through specific preimage configurations. Drawing from Kolmogorov's foundational work in computational complexity, this 2-hour seminar presents cutting-edge research while connecting it to classical theories in dynamical systems and automata theory.