Gallery of Square-Triangle Tilings
This page shows square-triangle tilings that have the following characteristics:
· The squares have 1 or 2 (of the 4 possible) substitution rules
· They are rotationally and reflectively symmetric
Each tiling has a fixed point or a pair of periodic points with period 2. For background on these tilings, see Square-Triangle Tilings.
Select each mandala to see more about the design.
|
Rules for tilings 1-4 PDF |
|
|
|
|
|
|
|
|
|
|
|
Rules for tilings 5-6 PDF |
|
|
|
Rules for tilings 7-10 PDF |
|
|
|
|
|
|
|
Tilings 11-14 PDF |
|
|
|
|
|
|
|
Tilings 15-18 PDF |
|
|
|
|
|
|
|
Tilings 19-22 PDF |
|
|
|
|
|
|
For the remaining tilings, I only include the inflation rules and mandalas. Select each mandala for a PDF.
|
Tilings 23-26 PDF |
Tiling 23 PDF |
Tiling 24 |
|
Tiling 25 |
Tiling 26 PDF |
|
|
Tilings 27-30 PDF |
Tiling 27 PDF |
Tiling 28 PDF |
|
Tiling 29 PDF |
Tiling 30 PDF |
|
|
Tilings 31-33 PDF |
Tiling 31 PDF |
Tiling 32 PDF |
|
Tiling 33 PDF |
|
|
|
Tilings 34-37 PDF |
Tiling 34 PDF |
Tiling 35 PDF |
|
Tiling 35 PDF |
Tiling 36 PDF |
Tiling 37 PDF |
Tiling 36 is the same as tiling 25 to the second inflation, but they are different at the third inflation (not shown).
|
Tilings 38-41 PDF |
Tiling 38 PDF |
Tiling 39 PDF |
|
Tiling 40 PDF |
Tiling 41 PDF |
|
|
Tilings 42-45 PDF |
Tiling 42 PDF |
Tiling 43 PDF |
|
Tiling 43 PDF |
Tiling 44 PDF |
Tiling 45 PDF |
|
Tilings 46-49 PDF |
Tiling 46 PDF |
Tiling 47 PDF |
|
Tiling 48 PDF |
Tiling 49 PDF |
|
|
Tilings 50-53 PDF |
Tiling 50 PDF |
Tiling 51 PDF |
|
Tiling 52 PDF |
Tiling 53 PDF |
|
|
Tilings 54-57 PDF |
Tiling 54 PDF |
Tiling 54 PDF |
|
Tiling 55 PDF |
Tiling 56 PDF |
Tiling 57 PDF |
The mandala for tiling 55 is the same as tiling 39 at iteration 2. They are different at iteration 3 (not shown).
|
Tilings 58-59 PDF |
Tiling 58 PDF |
Tiling 59 PDF |
Mandalas for tilings 58 and 59 are the same at the second iteration, but are different at the third iteration, not shown.
The images on these gallery are also on pinterest (but not the PDFs, and the numbering is close but does not exactly match).
Back to Gallery of Substitution Tilings
Copyright 2019-2020 by Jim Millar