A051023 Middle column of rule-30 1-D cellular automaton, from a lone 1 cell.

1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1

Offset: 0

Author

Eric W. Weisstein

Keywords

• nonn

Comments

A092539(n) gives the value of prefix of length n+1, seen as a binary number. - Reinhard Zumkeller, Jun 08 2013

Also middle column of rule 86 1-D cellular automaton, from a lone 1 cell, as rule 86 is the mirror image of rule 30. - Antti Karttunen, Oct 03 2019

Links

• Antti Karttunen, Table of n, a(n) for n = 0..100000 (terms 0..10000 from Reinhard Zumkeller)
• Pedro Hecht, PQC: R-Propping a Chaotic Cellular Automata, Univ. of Buenos Aires (Argentina, 2021).
• Erica Jen, Global properties of cellular automata, Journal of Statistical Physics 43 (1986), pp 219-242.
• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton.
• Eric Weisstein's World of Mathematics, Rule 30
• Eric Weisstein's World of Mathematics, Random Number
• Xiangdong Wen, A Billion Bits of the Center Column of the Rule 30 Cellular Automaton, 2019
• Stephen Wolfram, Announcing the Rule 30 Prizes, 2019
• Stephen Wolfram, A Million Bits of the Center Column of the Rule 30 Cellular Automaton, 2017
• Wolfram Mathematica, Cellular automata: Mathematica notebooks
• Index entries for sequences related to cellular automata
• Index entries for characteristic functions

Crossrefs

Cf. A070950, A269160 (rule 30), A071032, A269161 (rule 86).

Cf. A000035, A092539, A226474.

Cf. A327974 (adjacent bits xored), A327982 (partial sums), A327983 (run lengths).

Characteristic function of A327984 (gives the positions of ones in this sequence), A327985 (positions of zeros).

Cf. also A328100, A328101, A328102 (neighbor columns).

Cf. A365254 (converted to base 10).

Programs

Haskell

a051023 n = a070950 n n  -- Reinhard Zumkeller, Jun 06 2013

Mathematica

CellularAutomaton[30, {{1}, 0}, 101, {All, {0}}]//Flatten

PARI

A051023(n) = ((A110240(n)>>n)%2);
\\ Or for fast creation of b-files:
A051023write(up_to) = { my(s=1, n=0); for(n=0,up_to, write("b051023.txt", n, " ", ((s>>n)%2)); s = A269160(s)); }; \\ Antti Karttunen, Oct 03 2019

Formula

a(n) = A070950(n,n). - Reinhard Zumkeller, Jun 06 2013

a(n) = 1 - A226474(n). - Reinhard Zumkeller, Jun 08 2013

From Antti Karttunen, Oct 04 2019: (Start)

a(n) = A000035(floor(A110240(n) / 2^n)).

For n>= 2, a(n) = (A328100(n) OR A328101(n)) XOR A328101(1+n). ["Sideways evaluation"]

(End)

Extensions

Corrected from 64th term by Daniel B. Cristofani (cristofd(AT)hevanet.com), Jan 07 2004