Predicting Cellular Automata
Jameson Toole
Massachusetts Institute of Technology
Cambridge, MA
jltoole@mit.edu
Scott E. Page
University of Michigan
Ann Arbor, MI
Abstract
We explore the ability of a locally informed individual agent to predict the future state of a cell in systems of varying degrees of complexity using Wolfram's one-dimensional binary cellular automata. We then compare the agent's performance to that of two small groups of agents voting by majority rule. We find stable rules (class I) to be highly predictable, and most complex (class IV) and chaotic rules (class III) to be unpredictable. However, we find rules that produce regular patterns (class II) vary widely in their predictability. We then show that the predictability of a class II rule depends on whether it produces vertical or horizontal patterns. We comment on the implications of our findings for the limitations of collective wisdom in complex environments.
