Complex Systems

An Improved Generalized Enumeration of Substitution Systems Download PDF

Kenneth E. Caviness
Camille Morrow
Christen Case
Victoria Kratzke

Physics and Engineering Department
Southern Adventist University
Collegedale, TN 37315


The enumeration of all sequential substitution system rulesets is modified to include generalized substitution system rulesets. Unlike its predecessor, the new enumeration is one-to-one: each ruleset is guaranteed to appear exactly once in the new enumeration, which moreover possesses an elegant simplicity that allows jumps over increasingly longer undesired subsequences of many types. This process effectively results in an increased acceleration and greatly improved performance.

Keywords: sequential substitution system; enumeration

Cite this publication as:
K. E. Caviness, C. Morrow, C. Case and V. Kratzke, “An Improved Generalized Enumeration of Substitution Systems,” Complex Systems, 29(4), 2020 pp. 837–860.