Explore the fascinating intersection of fractal dimensions and Büchi automata in this 49-minute Fields Postdoc Colloquium talk by Alexi Block Gorman at The Fields Institute. Delve into formal definitions, automata theory, and regular languages before examining Büchi automata and ω-languages. Investigate the sets recognized by these automata and gain deeper insights into fractal dimensions through examples. Analyze scenarios where dimensions disagree and discover applications in Model Theory. This comprehensive lecture provides a rigorous mathematical foundation while bridging the gap between abstract concepts and practical applications in computer science and mathematics.