Grids and universal computations on one-dimensional cellular automata

This article shows how universal computations can be achieved on one-dimensional cellular automata. We are interested in intrinsic universality: we want a CA in which any other CA can be represented and simulated with no intermediate coding relevant to another computation model. We first abstract the space-time diagram in favor of the dependency graph. Then we show how such a dependency graph (via treillis automata) can be realized by what is called a grid, leading to a simple uniform simulation. Finally, we exhibit a very simple universal brick that can be used in grids to obtain an intrinsic universal CA.