A106642 A four-symbol four-at-a-time substitution with an ordering change: q=1.

1, 4, 4, 1, 4, 3, 3, 4, 4, 3, 3, 4, 1, 4, 4, 1, 4, 3, 3, 4, 3, 2, 2, 3, 3, 2, 2, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 2, 2, 3, 3, 2, 2, 3, 4, 3, 3, 4, 1, 4, 4, 1, 4, 3, 3, 4, 4, 3, 3, 4, 1, 4, 4, 1, 4, 3, 3, 4, 3, 2, 2, 3, 3, 2, 2, 3, 4, 3, 3, 4, 3, 2, 2, 3, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 2, 3, 3, 2, 2, 3, 2, 1, 1, 2, 2

Offset

0,2

Comments

This substitution gives two border-like 90-degree fractals, one (q=1) of which appears to tile. This substitution is a symmetrical doubling of the Levy's dragon-Heighway's dragon ordering.

Links

Table of n, a(n) for n=0..104.

Formula

1->{2, 1, 1, 2}, 2->q*{3, 2, 2, 3} + (1 - q)*{2, 3, 3, 2}, 3->{4, 3, 3, 4}, 4->q*{1, 4, 4, 1} + (1 - q)*{4, 1, 1, 4}.

Mathematica

q = 1; s[1] = {2, 1, 1, 2}; s[2] = q*{3, 2, 2, 3} + (1 -q)*{2, 3, 3, 2}; s[3] = {4, 3, 3, 4}; s[4] = q*{1, 4, 4, 1} + (1 - q)*{4, 1, 1, 4}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[4]

Crossrefs

Sequence in context: A055180 A030788 A087709 * A327855 A213056 A135012

Adjacent sequences: A106639 A106640 A106641 * A106643 A106644 A106645

Keyword

nonn,uned

Author

Roger L. Bagula, May 12 2005

Status

approved