Smallest PV

• Euclidean Windowed Tiling
• One Dimensional
• Plastic Number
• Polytopal Tiles
• Self-Similar Substitution

Info

The three letter substitution rule whose scaling is the smallest PV number, the Plastic Number which is a root of the polynomial $x^3 - x - 1 = 0$. Though it might not look it at first glance, the Rauzy fractal is connected. This can be shown using the method of A. Siegel described in [Sie04].

The Rauzy fractal:

Substitution Rule

Patch

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References

[Sie04]
Siegel, Anne
Pure discrete spectrum dynamical system and periodic tiling associated with a substitution
Ann. Inst. Fourier (Grenoble) 2004, 54, 2, pp. 341--381,

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