Harmonic evolutions on graphs

We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over Z2). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of evolutions are analyzed and classified. This construction can also be viewed as a certain topological generalization of cellular automata. MSC: 05C50, 15A33, 05C75, 05C85.

• Type: Journal
• Year: 2012
• Where: CORR
• Authors: Jerzy Kocik
• Keywords: Cellular Automata, CORR 2012, Digraphs, Education, Laplacian