A364241 a(n) is the initial transient (converted to base 10), before the periodic part, on the n-th diagonal from the left of rule-30 1-D cellular automaton, when started from a single ON cell, or -1 if there is no transient part.
-1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 4, 9, 0, 228, 63, 1241, 69, 7609, 2944, 11356, 255, 28487, 30890, 42037, 24160, 104333, 19167, 132196, 25361, 1042145, 473564, 4512243, 153187, 258856349, 2950249, 353554884, 104435283, 26762321451, 2005002052
Offset: 1
Examples
In the following diagram, showing the first 22 evolution steps of the CA, three diagonals are highlighted, along with their transient and periodic parts (the rest of the CA is represented by hyphens, for better visualization).
.
3rd diagonal
__ Transient = 1
- / Repeat = 0
--1 a(3) = 1
--0--
--0---- 12th diagonal
--0------ __ Transient = 01
--0--------/ Repeat = 0010
--0--------0- a(12) = 1
--0--------1---
--0--------0----- __ 20th diagonal
--0--------0-------/ Transient = 01000101
--0--------1-------0- Repeat = 1100
--0--------0-------1--- a(20) = 69
--0--------0-------0-----
--0--------0-------0-------
--0--------1-------0---------
--0--------0-------1-----------
--0--------0-------0-------------
--0--------0-------1---------------
--0--------1-------1-----------------
--0--------0-------1-------------------
--0--------0-------0---------------------
--0--------0-------0-----------------------
--0--------1-------1-------------------------
.
Links
- Paolo Xausa, Table of n, a(n) for n = 1..1000
- Michael Brunnbauer, Diagonals in elementary cellular automaton 30, 2019 (local PDF copy, with author's permission).
- Eric S. Rowland, Local Nested Structure in Rule 30, Complex Systems 16 (2006), pp. 239-258.
- Eric Weisstein's World of Mathematics, Rule 30.
- Stephen Wolfram, Notes on chapter 2, Rule 30, from A new kind of science online, Wolfram Media, 2002.
- Index entries for sequences related to cellular automata
Comments