# Generating 2D Metallic-Mean Quasiperiodic Tilings with NKS Substitution Rules

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This Demonstration shows an alternative, computationally more efficient way of generating the colored two-dimensional (2D) quasiperiodic square tilings reported in [1]. The computation of the tilings in this Demonstration is achieved by using a set of substitution rules on colored squares for the Fibonacci (or golden ratio) system based on *A New Kind of Science* [2, Notes. Chapter 5: Section 4].

Contributed by: Jessica Alfonsi (October 2019)

(Padova, Italy)

Open content licensed under CC BY-NC-SA

## Details

Snapshot 1: square tiling of a 2D quasiperiodic system obtained from Fibonacci substitution rule (), mesh edge highlighting enabled and grayscale set of colors as reported in [2]

Snapshot 2: square tiling of a 2D quasiperiodic system obtained from Fibonacci substitution rule () with nesting index and default set of colors

Snapshot 3: square tiling of a 2D quasicrystal obtained from silver-mean substitution rule () with nesting index and default set of colors

Snapshot 4: square tiling of a 2D quasicrystal obtained from bronze-mean substitution rule () with nesting index and random set of colors

References

[1] J. Alfonsi. "Coloring 2D Metallic-Mean Quasicrystal Tilings with a Mesh-Based Method" from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/Coloring2DMetallicMeanQuasicrystalTilingsWithAMeshBasedMetho.

[2] S. Wolfram, *A New Kind of Science*, Champaign, IL: Wolfram Media, Inc., 2002. www.wolframscience.com/nks/notes-5-4--substitution-systems-based-on-other-shapes (*NKS|Online*).

[3] V. W. De Spinadel, "The Metallic Means Family and Art," *Journal of Applied Mathematics*, 3(1), 2010 pp. 53–64. www.aplimat.com/files/Journal_volume_3/Number_1.pdf.

## Snapshots

## Permanent Citation