A363344 Array read by ascending antidiagonals: T(n,k) is the value of the k-th cell on the n-th diagonal from the left of rule-30 1-D cellular automaton, when started from a single ON cell, with n, k >= 1.

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

Offset

1

Comments

Equivalently, diagonals from the right of rule-86 cellular automaton, which is the left-right symmetric version of rule-30 cellular automaton.

For the sequence of eventual periods of the diagonals and initial transients, see A363345 and A363346, respectively.

Links

Paolo Xausa, Table of n, a(n) for n = 1..11325 (antidiagonals 1..150 of the array, flattened).

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.

Index entries for sequences related to cellular automata

Example

The following diagram illustrates how the array is built.
.
            1               Diagonals from the left of rule-30 CA
             \              are the same as diagonals from the right
          1 1 1             of rule-86 CA, shown here.
           \ \ \
        1 0 0 1 1
         \ \ \ \ \
      1 1 1 1 0 1 1
         \ \ \ \ \ \
    1 0 0 0 1 0 0 1 1
           \ \ \ \ \ \	
  1 1 1 0 1 1 1 1 0 1 1     Array begins:
             \ \ \ \ \ \___ 1 1 1 1 1 1 1 1 1 1 1 1 ... (period 1)
       ...    \ \ \ \ \____ 1 1 1 1 1 1 1 1 1 1 1 1 ... (period 1)
               \ \ \ \_____ 1 0 0 0 0 0 0 0 0 0 0 0 ... (period 1)
                \ \ \______ 0 1 0 1 0 1 0 1 0 1 0 1 ... (period 2)
                 \ \_______ 1 1 1 1 1 1 1 1 1 1 1 1 ... (period 1)
                  \________ 1 0 1 0 1 0 1 0 1 0 1 0 ... (period 2)
                            ...

Mathematica

A363344list[dmax_]:=Module[{ca=CellularAutomaton[86, {{1}, 0}, dmax-1], a}, a=Array[Drop[Diagonal[ca, #], Floor[(dmax-#)/2]]&, dmax, 0]; Array[Diagonal[a, #]&, dmax, 1-dmax]]; A363344list[15] (* Generates 15 antidiagonals *)

Crossrefs

Cf. A070950.

Cf. A363345 (periods of diagonals), A363346 (lengths of transients), A363343 (diagonals from the right).

Sequence in context: A070950 A071031 A187037 * A327866 A336477 A190230

Adjacent sequences: A363341 A363342 A363343 * A363345 A363346 A363347

Keyword

nonn,tabl

Author

Paolo Xausa, May 28 2023

Status

approved