Work and Research Interests
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Cellular automata systems have been established as a suitable constructive framework for the general purpose of modeling spatially extended complex systems. Such systems are based on a discrete grid/lattice of cells, which naturally represent spatial extent. Each cell within the lattice evolves from one discrete state to another, in discrete time, according to specified rules. The transition rules are applied locally, as a function of the current state of the cell as well as the states of the neighbouring cells. A CA system is well defined when the state space and the local dynamical rules are unambiguously specified.
The simplest class of CA systems, aptly called Elementary CA, are 1D binary state systems, i.e. a row of cells, each of which can be either 0 or 1. The smallest neighbourhood consists of 3 cells (one cell on each side of a given cell), and the transition rules are specified by enumerating all possible configurations of a row of 3 cells with 2 states each. Even though the definition of the system is simple, the configurations which emerge after sufficient time can form extremely intricate patterns.
Another well studied system is known as the Game of Life. This system is a 2D binary state CA, with transition rules which may be described as an abstraction of the dynamics of competitive survival. This system has generated a lot of curiosity since the discovery of stable periodic objects. Subsequently, many interesting structures have been discovered, such as self propagating structures, and complex structures which generate simpler structures.
Conway designed the rules for the well known cellular automata called Game of Life. The incredibly complex structures that are created, sustained and destroyed with this set of rules have, and continue, to generate curiosity and inspire research.
The systems discussed above have been significant for our understanding of abstract computation as well. A specific Elementary CA, known as Rule 30, as well as Game of Life, have been proven to be Turing Complete, and therefore capable of universal computation.
Beyond questions of computability, CA systems have played a significant role in demonstrating mechanisms for the phenomenon of self-organized criticality, and the consequent generation of power law distributions. The Sandpile model is a prototypical CA model for driven, dissipative systems. The system naturally tends towards a critical state, beyond which the response of the system becomes uncorrelated to the perturbation received by the system. Such characteristics have been observed in certain natural and engineered systems, which comprise of multiple interacting dynamical units. The Sandpile model was one of the first to elucidate a concrete dynamical mechanism which leads to collective emergent phenomena with these characteristic signatures.
