Cayley Graphs: Mapping Algebraic Symmetry in Le Santa’s Design
At the intersection of algebra and visual design lies the powerful concept of Cayley graphs—structured networks that illuminate symmetry through graph theory. These graphs transform abstract group generators and relations into spatial maps, revealing the underlying order of complex patterns. In systems like Le Santa’s design, Cayley graphs serve as a formal bridge connecting mathematical symmetry to tangible aesthetic form.
1. Introduction: Cayley Graphs as Visual Bridges Between Algebra and SymmetryCayley graphs are mathematical structures defined as either directed or undirected graphs, where nodes represent elements of a group and edges encode multiplication by generators—operators that drive symmetry transformations. Each node corresponds to a unique group element,