5 ms·
Amazing... learning of the existence/term of polyominoes is a breakthrough for me. I’ve recently been working on developing a novel statistical test to quantif
by bransonf 6y ago
Amazing... learning of the existence/term of polyominoes is a breakthrough for me.
I’ve recently been working on developing a novel statistical test to quantify sensitivity to the modifiable areal unit problem (MAUP). The limiting factor has been the ability to efficiently generate arbitrarily shaped polygons on a lattice at random. In essence, this is needed to stochastically reallocate a spatial characteristic and measure variance.
Apparently, the exact solution I’m looking for is Donald Knuth’s algorithm X [0]. And I also found this interesting application of the algorithm [1].
I simply cannot express how much my curiosity has just peaked. Moreover, I now have reason to cite both Solomon Golomb and Donald Knuth in a paper.
[0] https://en.m.wikipedia.org/wiki/Knuth%27s_Algorithm_X https://en.m.wikipedia.org/wiki/Knuth%27s_Algorithm_X
[1]
https://gfredericks.com/blog/99 https://gfredericks.com/blog/99
- kian 6y agoCuriosity peaking (I have also seen peeking) is quite an interesting mondegreen for curiosity 'piquing'. The latter means 'stimulating' or 'aggravating', whereas the former implies that when you hear about something for the first time your curiosity is at a maximum - which is a fun interpretation :)
- sidpatil 6y agoI wouldn't be surprised if peak and pique have similar etymology.
- knuthsat 6y agoYou might find zero suppressed binary decision diagrams (ZDDs) useful. They also allow simple random generation of all kinds of objects (even constrained ones). Knuth adjusted his algorithm X for ZDD and got some nice speedups.
- amongwhales 6y agoI had never seen polyominoes used professionally for mathematics. However, I was reminded of seeing them in the teen novel Chasing Vermeer [0]. [0]https://en.m.wikipedia.org/wiki/Pentomino#Literature https://en.m.wikipedia.org/wiki/Pentomino#Literature
- melonmouse 6y agoI made a game about polyominoes: https://melonmouse.itch.io/polyominoes https://melonmouse.itch.io/polyominoes If you try it out, please let me know what you think :) P.S. work on that led to a sequence on the Online Encyclopedia of Integer Sequences: https://oeis.org/A239658 https://oeis.org/A239658
- ballenf 6y agoOne QOL consideration: consider allowing the last placed piece to be moved in one click. That is, if you click while "at capacity" the last placed piece gets removed and placed where you click.