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A364240
a(n) is the periodic part (converted to base 10), on the n-th diagonal from the left of rule-30 1-D cellular automaton, when started from a single ON cell.
3
1, 1, 0, 1, 1, 2, 2, 0, 12, 1, 6, 2, 13, 11, 6, 3, 11, 8, 6, 12, 6, 7, 3, 2, 8, 9, 14, 13, 0, 180, 1, 90, 74, 25, 156, 224, 98, 250, 123, 12, 20, 239, 215, 138, 20, 12, 159, 192, 58, 253, 139, 86, 195, 164, 25, 28, 48, 235, 159, 162, 213, 152, 25, 8, 14, 239
OFFSET
1,6
COMMENTS
See A363345 for the periods.
LINKS
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.
EXAMPLE
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) = 0
--0--
--0---- 12th diagonal
--0------ __ Transient = 01
--0--------/ Repeat = 0010
--0--------0- a(12) = 2
--0--------1---
--0--------0----- __ 20th diagonal
--0--------0-------/ Transient = 01000101
--0--------1-------0- Repeat = 1100
--0--------0-------1--- a(20) = 12
--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-------------------------
.
MATHEMATICA
A364240list[nmax_]:=With[{ca=CellularAutomaton[86, {{1}, 0}, {2nmax, {1-nmax, nmax}}]}, Array[FromDigits[Last[FindTransientRepeat[Drop[Diagonal[ca, nmax-#], Ceiling[(#-1)/2]], 2]], 2]&, nmax]]; A364240list[100]
CROSSREFS
Cf. A070950.
Cf. A363344 (diagonals), A363345 (periods), A363346 (length of transients), A364241 (transients).
Sequence in context: A335987 A285539 A285783 * A117270 A244137 A354127
KEYWORD
nonn,base
AUTHOR
Paolo Xausa, Jul 15 2023
STATUS
approved