It from Bit: Cellular Automata, Driven Ising Model, and Emergent Computation

We explored emergent computation within two systems — cellular automata (CA) and a driven Ising model. We attempted to generate emergent computation with a CA using a genetic algorithm, with the aim of understanding general conditions on information processing dynamics which increase computational capacity. Specifically, we aim to search the space of CAs to identify minimal computational units, which may in turn be used to execute specific computational tasks or optimize further search for collective computational behavior. In order to select for CAs with more computational capacity, we use an objective function defined in terms of dual total correlation (DTC), an information-theoretic quantity capturing the information in higher-order correlations between cells in a given spatial (and temporal) region of the time-dependent CA grid. The genetic algorithm evolves a population of CA update rules by testing average performance over a range of initial conditions, creating a new population favoring more successful rules, and iterating over a number of generations. In addition, we have explored stochastic thermodynamics within a driven Ising model. This initial investigation has given us insight into thermodynamic relations present that will be beneficial for exploring this system’s computational capacity in future work. In this preliminary study, the work distribution produced by many realization under the influence of a time-symmetric drive is consistent with known fluctuation relations in the field of stochastic thermodynamics. In future work, we hope to explore dissipative adaptation as a potential mechanism for promoting emergent computation.