  We introduce several concepts such as prime and composite rule, tools and
methods for causal composition and decomposition. We discover and prove new
universality results in ECA, namely, that the Boolean composition of ECA rules
51 and 118, and 170, 15 and 118 can emulate ECA rule 110 and are thus
Turing-universal coupled systems. We construct the 4-colour Turing-universal
cellular automaton that carries the Boolean composition of the 2 and 3 ECA
rules emulating ECA rule 110 under multi-scale coarse-graining. We find that
rules generating the ECA rulespace by Boolean composition are of low complexity
and comprise prime rules implementing basic operations that when composed
enable complex behaviour. We also found a candidate minimal set with only 38
ECA prime rules---and several other small sets---capable of generating all
other (non-trivially symmetric) 88 ECA rules under Boolean composition.
