For now some resources you might find interesting.
A tiling is a covering of the whole plane with non-overlapping tiles, each of which is a topological disc. The classic work on tilings is Tilings and Patterns by Grunbaum, Shephard. A list with other books on the subject can be found here.
M.C. Escher used tilings in his graphics work in an ingenious way. This book contains a nice collection of the work of Escher.
It's interesting to note that in Escher's time (1901-1972) there was hardly any mathematical theory about tilings. The foundational work on tilings was published five years after Escher died. Yet from Escher's work it is clear that he understood tilings, and the related line symmetries ( Frieze Patterns ), lattices and plane symmetries ( Wallpaper Patterns ) as no other.
If you are interested in puzzles at all it's likely that you came across Jaap's Puzzle Page, a vast resource of information regarding puzzles. The website is maintained by Jaap Scherphuis. You'll find his YouTube site here with many puzzle demonstrations.
To my astonishment Scherphuizen also maintains an impressive collection of tilings on a Tilings Page. His tilings demonstrations Java Applet is as impressive which you'll find on the same page.
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| 'Pentagon Flower' ( background tiling is the [4,8,8] Laves tiling ) (c) nilo de roock 2012 |
Thanks for the link to my tiling page.
ReplyDeleteI've not done much work on it recently. The programs I have are too slow to make much more progress, and their results are too labour intensive to sort through for the valid tilings. I've been meaning to rewrite most of it some day, but am too busy with other hobbies at the moment.
P.S. A small correction: My youtube videos are mostly magic rather than puzzles.