Abstract
In the context of quantum gravity theories, several researchers have proposed causal sets as appropriate discrete models of spacetime. We investigate families of causal sets obtained from two simple models of computation – 2D Turing machines and network mobile automata – that operate on 'high-dimensional' supports, namely 2D arrays of cells and planar graphs, respectively. We study a number of quantitative and qualitative emergent properties of these causal sets, including dimension, curvature and localized structures, or 'particles'. We show how the possibility to detect and separate particles from background space depends on the choice between a global or local view at the causal set. Finally, we spot very rare cases of pseudo-randomness, or deterministic chaos; these exhibit a spontaneous phenomenon of 'causal compartmentation' that appears as a prerequisite for the occurrence of anything of physical interest in the evolution of spacetime.