2015/03/04 by N. J. A. Sloane, Sloane, N. J. A.
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · Mathematics · #37B15 #Cellular Automata and Applications #Combinatorics (math.CO) #DNA and Biological Computing #FOS: Mathematics #Primary 11B85 #Quasicrystal Structures and Properties #math.CO #msc:11B85 #msc:37B15
paper · pdf · doi:10.48550/arxiv.1503.01168
20 pages, 26 references, 8 figures, 5 tables
arxiv created 2015/03/04 · openalex publication_date 2015/03/04 · arxiv updated 2015/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If a cellular automaton (CA) is started with a single ON cell, how many cells will be ON after n generations? For certain "odd-rule" CAs, including Rule 150, Rule 614, and Fredkin's Replicator, the answer can be found by using the combination of a new transformation of sequences, the run length transform, and some delicate scissor cuts. Several other CAs are also discussed, although the analysis becomes more difficult as the patterns become more intricate.