Non-maximal sensitivity to synchronism in elementary cellular automata: Exact asymptotic measures

Nineteen elementary cellular automata rules (and their conjugation, reflection, reflected-conjugation) have been proven not maximum sensitive to synchronism, i.e. they do not have a different dynamics for each (non-equivalent) block-sequential update schedule (defined as ordered partitions of cell positions). In this work we present exact measurements of the sensitivity to synchronism for these rules, as functions of the size. These exhibit a surprising variety of values and associated proof methods, such as the isomer pairs of rule 128, and the connection to the bisection of Lucas numbers of rule 8.