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A105500
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Trajectory of 1 under the morphism 1->{1,2}, 2->{3,2}, 3->{3,4}, 4->{1,4}.
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5
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1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 1, 4, 3, 4, 3, 2, 3, 4, 1, 4, 1, 2, 1, 4, 3, 4, 1, 4, 3, 4, 3, 2, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 3, 4, 1, 4, 3, 4, 3, 2, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 1
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OFFSET
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0,2
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COMMENTS
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Harter-Heighway dragon when interpreting 1, 2, 3, and 4 respectively as unit edge to right, up, left, and down. - Joerg Arndt, Jun 03 2021
The characteristic polynomial of the transition matrix is x^4-4*x^3+6*x^2-4*x = x*(x-2)*(x^2 - 2*x + 2).
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LINKS
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F. M. Dekking, Recurrent sets, Advances in Mathematics, vol. 44, no. 1 (1982), 78-104; page 89, section 4.5.
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FORMULA
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MATHEMATICA
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Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2}, 2 -> {3, 2}, 3 -> {3, 4}, 4 -> {1, 4}} &], {1}, 7]]
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PROG
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(Python)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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