File:Plastic5 Rauzy sqr.png
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Captions
Captions
Rauzy fractal for a substitution rule associated with the sequence 1,1,1,3,5,8,15,26,45,80,...
Summary
[edit]| Description |
English: The production rule is (a ↦ ab) (b ↦ c) (c ↦ aad) (d ↦ e) (e ↦ a) with initiator e, iterated for 27 generations. l(wn) = A193147(n−7) + ... + A193147(n−3). The incidence matrix has reducible characteristic polynomial f(x) = x5 − x4 − 2x2 − 1 and dominant eigenvalue ρ2 ≈ 1.75488 (the plastic ratio-squared). The central tile and its five subtiles have areas in the ratios ρ10 + ρ5 : ρ8 : ρ6 : ρ4 : ρ2 : 1. The viewport height is 2.3 and the origin is at the centre of the spiral. Empirically, the fractal boundary has box-counting dimension 1.11. Conjecturally, with dimbox(fb) ≈ ½logρ(λ), λ is the real solution of λ3 = λ2 + 3. |
| Date | |
| Source | Own work |
| Author | Zilverspreeuw |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
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| current | 14:41, 18 June 2024 | 1,738 × 2,000 (17 KB) | Zilverspreeuw (talk | contribs) | A bit brighter | |
| 15:47, 15 June 2024 | 1,738 × 2,000 (16 KB) | Zilverspreeuw (talk | contribs) | color balance | ||
| 15:43, 14 June 2024 | 1,738 × 2,000 (16 KB) | Zilverspreeuw (talk | contribs) | Uploaded own work with UploadWizard |
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