Percolation/Site percolation/J: Difference between revisions
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<code>groups</code> uses a sum fold on successive prefixes to identify regions of contiguous bits.
<lang j>
* 2
1 0
(2 </\ 0, *) 2 0 2 0 1 0 1 0 0 1 1 1 1 1 0
1 0 1 0 1 0 1 0 0 1 0 0 0 0 0
([: +/\ 2 </\ 0, *) 2 0 2 0 1 0 1 0 0 1 1 1 1 1 0
1 1 2 2 3 3 4 4 4 5 5 5 5 5 5</lang>
<code>ooze</code> propagates 2s from its right argument to adjacent groups of non-zero locations in its left argument.
Line 33 ⟶ 37:
2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 ([ >. [ +&* [ * [: ; groups@[ <@(* * 2 < >./)/. +) 0 0 1 1 1 1 0 2 0 2 0 1 1 1 1
2 0 2 0 1 0 1 0 0 2 2 2 2 2 0</lang>
Note that u/. uses the key in the left argument to gather corresponding values from the right argument (which are then processed by <code>u</code>).
<lang j> 2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 (groups@[ </. +) 0 0 1 1 1 1 0 2 0 2 0 1 1 1 1
┌───┬───┬───┬─────┬───────────┐
│2 0│3 1│2 1│1 2 0│3 1 2 2 2 1│
└───┴───┴───┴─────┴───────────┘
2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 (groups@[ <@(>./)/. +) 0 0 1 1 1 1 0 2 0 2 0 1 1 1 1
┌─┬─┬─┬─┬─┐
│2│3│2│2│3│
└─┴─┴─┴─┴─┘
2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 (groups@[ <@(2 < >./)/. +) 0 0 1 1 1 1 0 2 0 2 0 1 1 1 1
┌─┬─┬─┬─┬─┐
│0│1│0│0│1│
└─┴─┴─┴─┴─┘
2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 (groups@[ <@(* * 2 < >./)/. +) 0 0 1 1 1 1 0 2 0 2 0 1 1 1 1
┌───┬───┬───┬─────┬───────────┐
│0 0│1 1│0 0│0 0 0│1 1 1 1 1 1│
└───┴───┴───┴─────┴───────────┘</lang>
We use +&* because 1 +&* 2 is 2, but also 2 +&* 2 is 2:
Line 178 ⟶ 201:
2 2 2 0 2 2 0 0 2 0 2 0 0 1 1</lang>
(^:_ repeats an operation until it reaches a [[wp:Fixed_point_(mathematics)|fixed point]]. In other words, it's basically a while loop.)
<code>trial</code> generates an arbitrary connection matrix and runs percolate on it. You'll typically get a different result from each trial.
Line 231 ⟶ 254:
1 1 0 1 0 1 1 1 1 1 1 0 1 1 0
0 1 1 1 0 0 1 1 0 1 1 0 0 0 0
1 1 0 1 0 1 1 1 1 0 0 1 1 1 0
0.6 percolate@([ >: ] ?@$ 0:) 15 15
0 0 0 0 2 2 2 2 2 0 2 0 0 0 2
0 1 0 2 0 2 2 0 2 0 2 2 0 0 0
1 0 2 2 2 2 2 2 2 0 0 2 0 0 1
0 2 2 0 2 0 2 0 2 0 2 2 2 0 1
2 2 2 2 0 2 2 2 2 0 2 2 0 0 1
2 2 2 0 1 0 2 2 0 0 2 2 2 2 0
0 0 2 2 0 0 2 2 2 0 2 2 0 2 2
0 2 2 0 0 2 2 2 2 2 0 2 2 0 2
0 2 0 0 0 2 0 0 0 0 0 2 2 0 0
0 2 0 2 2 2 2 0 2 2 2 2 0 0 0
0 2 2 2 2 2 0 0 2 2 2 0 1 0 2
2 0 2 0 0 0 2 2 0 0 0 0 0 0 2
2 2 2 2 2 2 2 2 2 2 2 2 0 2 2
0 0 2 2 2 2 0 2 2 0 0 2 2 2 0
0 1 0 0 2 0 2 2 0 0 1 0 2 0 1</lang>
<code>simulate</code> runs a sequence of 15 by 15 trials and averages them. Since each trial is different, each run of simulate is different.
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