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File:Supersilver Rauzy baa.png

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English: The production rule is (a ↦ baa) (b ↦ c) (c ↦ a) with initiator b, iterated for 20 generations. The incidence matrix M [2,0,1; 1,0,0; 0,1,0] has characteristic polynomial f(x) = x3 − 2x2 − 1 and dominant eigenvalue ς = 2.20557 (the supersilver ratio). The central tile and its three subtiles have areas in the ratios ς2 ς 1 : ς2 : ς : 1. The viewport height is 2.7 and the origin is at the cross. Empirically, the fractal boundary has box-counting dimension 1.22. Conjecturally, with dimbox(fb) ≈ 2logς(λ), λ is the positive solution of λ3 = 2λ 1, thus λ = golden ratio φ.
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Author Zilverspreeuw

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Captions

Rauzy fractal for a substitution rule associated with the third-order Pell sequence.

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17 May 2024

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Date/TimeThumbnailDimensionsUserComment
current10:15, 5 June 2024Thumbnail for version as of 10:15, 5 June 20241,700 × 2,000 (23 KB)Zilverspreeuwcolors
15:55, 20 May 2024Thumbnail for version as of 15:55, 20 May 20241,500 × 2,000 (17 KB)Zilverspreeuwcolour
15:00, 17 May 2024Thumbnail for version as of 15:00, 17 May 20241,500 × 2,000 (17 KB)ZilverspreeuwUploaded own work with UploadWizard

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