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

Abstract: In [11] and [13] the authors showed that elementary cellular automata rules 0, 3, 8, 12, 15, 28, 32, 34, 44, 51, 60, 128, 136, 140, 160, 162, 170, 200 and 204 (and their conjugation, reflection, reflected-conjugation) are 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 special pairs of rule 128, and the connection to the bissection of Lucas numbers of rule 8.