Timeline for Soft question: mathematics about truchet tiles
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 17 at 23:23 | comment | added | David Feldman | Suppose one has a random Truchet having tiles decorated with quarter circles. Pick a tile and a direction and follow the meander. This constitutes a random walk on a lattice. As such, one expects surely get to distance $t$ from the origin at time asymptotic to $ct^2$, for some $c$ (unless the meander closes). But the path is self-avoiding, so at time $ct^2$ it has filled that many cells. So has the disjoint meander in the other direction. I expect it's easy to deduce a contradiction to all this happening with positive probability. | |
| Jan 22, 2015 at 14:01 | answer | added | Paul Zinn-Justin | timeline score: 8 | |
| Jan 19, 2015 at 15:13 | comment | added | Joseph O'Rourke | This MO question explored an analogous process: "Longest of random worm-like paths in $\mathbb{Z}^2$." | |
| Jan 19, 2015 at 14:58 | comment | added | john mangual | without boundary conditions, these become questions about the Ising model on a square lattice, see Discrete Complex Analysis and Probability by Stanislav Smirnov. | |
| Jan 19, 2015 at 14:52 | comment | added | zemora | @johnmangual:thanks,I have this file at hand but I do not know the background(statistical physics,conformal field theory,etc.)also it seems that the author means tiling on the semi-infinite cylinder, not quite on the square grid | |
| Jan 19, 2015 at 14:36 | comment | added | john mangual | lpthe.jussieu.fr/~pzinn/semi/miwa.pdf | |
| Jan 19, 2015 at 13:48 | history | edited | user9072 |
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| S Jan 19, 2015 at 13:44 | history | suggested | JRN | CC BY-SA 3.0 |
Included picture
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| Jan 19, 2015 at 13:36 | review | Suggested edits | |||
| S Jan 19, 2015 at 13:44 | |||||
| Jan 19, 2015 at 13:28 | comment | added | Wolfgang | As a side note: you might appreciate the game "Slant" in Simon Tatham's Portable Puzzle Collection. chiark.greenend.org.uk/~sgtatham/puzzles | |
| Jan 19, 2015 at 12:51 | history | asked | zemora | CC BY-SA 3.0 |