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- A legal tiling is defined to be a tiling which can be continued to cover the infinite plane.
- An unconnected tiling is defined to be a tiling containing two or more subtilings that are not connected to each other at any edges.
- When in show illigally placed tiles mode a tiling will be deemed illegal if it cannot be continued to cover the infinite plane, or if the tiling is unconnected.
- Conflicting uses of the words inflation and deflation appear in Penrose tiling texts. Grünbaum and Shephard1 defines inflation as increasing the size of the tiles and then decomposing them into tiles of the original size. This corresponds to pressing the zoom in button once and the decompose tiles button once. Deflation corresponds to pressing the zoom out button once and the compose tiles button once.
- After modifying a tiling the application loops through every tile and records which of the other tiles are its neighbour. Certain functions require this record. This process may take several seconds when decomposing large tilings.
- Composing large tilings may take more than one hour.
- When in show illigally placed tiles mode it may take more than one hour to determine if a large tiling is legal.
- When the add forced tiles at each vertex button is pressed the application loops through every vertex and places any forced tiles. Neighbouring vertices, which can sometimes force more tiles, are not considered when forcing tiles around the current vertex.
1. Grünbaum B, Shephard GC. Patterns and Tilings. 2nd ed. Mineola, New York: Dover Publications, Inc; 2016.
Page created by Kevin Bertman, http://www.mrbertman.com.