Computing on Rings

In this paper, we will review the developing features of computations based on rings. Particularly, we will analyse what kinds of interaction occur between gliders travelling on a ‘cyclotron’ cellular automaton derived from a catalog of collisions. We will demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of some simple computing models. Gliders in one-dimensional cellular automata are compact groups of non-quiescent patterns translating along an automaton lattice. They are cellular-automaton analogous to localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. So, they can be represented as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We present a number of complex one-dimensional cellular automata with such features.