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A106147 A Levy dragon -Heighway's dragon two state 4-symbol substitution : q=1 state Levy dragon : q=0 state Heighway's dragon: Characteristic Polynomial:x^4-4*x^3+6*x^2-4*x. 0
1, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 4, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 4, 3, 2, 2, 1, 2, 1, 1, 4, 2, 1, 1, 4, 1, 4, 4, 3, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 4, 3, 2, 2, 1, 2, 1, 1, 4, 2, 1, 1, 4, 1, 4, 4, 3, 3, 2, 2, 1, 2, 1, 1, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This result shows the transform ordering is very important. This concept was inspired by the Riddle IFS that gives the Twin dragon, Levy's dragon and Heighway's dragon by rotation of one of the two transforms.

LINKS

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

F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no.1, April 1982, page 85, section 4.1.

FORMULA

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

MATHEMATICA

q=1 s[1] = {2, 1}; s[2] = q*{3, 2} + (1 - q)*{2, 3}; s[3] = {4, 3}; s[4] = q*{1, 4} + (1 - q)*{4, 1}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[8]

CROSSREFS

Sequence in context: A020805 A200587 A307836 * A202393 A073321 A055620

Adjacent sequences:  A106144 A106145 A106146 * A106148 A106149 A106150

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, May 07 2005

STATUS

approved

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Last modified October 16 05:35 EDT 2019. Contains 328044 sequences. (Running on oeis4.)