Abstract geometrical computation 4: Small Turing universal signal machines

This paper provides several very small signal machines able to perform any computation—in the classical understanding—generated from Turing machines, cellular automata and cyclic tag systems. A halting universal signal machine with 13 meta-signals and 21 collision rules is presented (resp. 15 and 24 for a robust version). If infinitely many signals are allowed to be present in the initial configuration, five meta-signals and seven collision rules are enough to achieve non-halting weak universality (resp. six and nine for a robust version).