Monthly Archives: January 2023

Tilings of 5-Fold Rotational Symmetry: VI. Substitution at Diagonals

Posted on January 27, 2023 by Peter Stampfli

As we have seen previously, the substitution for a tiling puts a narrow child rhombus with its short diagonal at the border of the inflated parent rhombus. This cuts the rhombus into two triangles. One of them will be inside … Continue reading →

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Tilings of 5-Fold Rotational Symmetry: V. Conservation of Area in Substitution

Posted on January 13, 2023 by Peter Stampfli

The substitution method fills the inflated parent tile with child tiles having no overlap or gaps. Thus, the total area of the child tiles has to be exactly equal to the area of the parent tile. This allows us to … Continue reading →

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Tilings of 5-Fold Rotational Symmetry: IV. Algebraic Integers

Posted on January 6, 2023 by Peter Stampfli

In the last post we have seen that inflation factors r for the substitution method are elements of the integer ring ℤ[τ]={h+k τ | h,k ∊ ℤ}, where τ is the golden ratio. Trivially, the sum of two elements of … Continue reading →

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Tilings of 5-Fold Rotational Symmetry: III. Substitution Method

Posted on January 5, 2023 by Peter Stampfli

Trying to extend the rosette does not work, instead one better uses the substitution method. It increases the size of the rhombi by an inflation factor r to get large parent tiles which are then replaced by child tiles of … Continue reading →

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