Percolation/Site percolation/J: Difference between revisions
(Explanation, with examples, of J implementation.) |
mNo edit summary |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 10: | Line 10: | ||
<code>groups</code> uses a sum fold on successive prefixes to identify regions of contiguous bits. |
<code>groups</code> uses a sum fold on successive prefixes to identify regions of contiguous bits. |
||
<lang j> |
<lang j> 2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 |
||
2 0 2 0 1 0 1 0 0 1 1 1 1 1 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 1 1 1 1 0 |
|||
(0, *) 2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 |
|||
0 1 0 1 0 1 0 1 0 0 1 1 1 1 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. |
<code>ooze</code> propagates 2s from its right argument to adjacent groups of non-zero locations in its left argument. |
||
| Line 32: | Line 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 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> |
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: |
We use +&* because 1 +&* 2 is 2, but also 2 +&* 2 is 2: |
||
| Line 177: | Line 201: | ||
2 2 2 0 2 2 0 0 2 0 2 0 0 1 1</lang> |
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]].) |
(^:_ 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. |
<code>trial</code> generates an arbitrary connection matrix and runs percolate on it. You'll typically get a different result from each trial. |
||
| Line 230: | Line 254: | ||
1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 |
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 |
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 |
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. |
<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. |
||
Latest revision as of 13:07, 19 August 2015
<lang J>groups=:[: +/\ 2 </\ 0 , * ooze=: [ >. [ +&* [ * [: ; groups@[ <@(* * 2 < >./)/. + percolate=: ooze/\.@|.^:2^:_@(* (1 + # {. 1:))
trial=: percolate@([ >: ]?@$0:) simulate=: %@[ * [: +/ (2 e. {:)@trial&15 15"0@#</lang>
Explanation:
groups uses a sum fold on successive prefixes to identify regions of contiguous bits.
<lang j> 2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 2 0 2 0 1 0 1 0 0 1 1 1 1 1 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 1 1 1 1 0
(0, *) 2 0 2 0 1 0 1 0 0 1 1 1 1 1 0
0 1 0 1 0 1 0 1 0 0 1 1 1 1 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>
ooze propagates 2s from its right argument to adjacent groups of non-zero locations in its left argument.
<lang j> 2 0 2 0 1 0 1 0 0 1 1 1 1 1 0 + 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@[ <@(* * 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│ └───┴───┴───┴─────┴───────────┘
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
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 2 0 0 0 0 0 0 1 1 1 1 1 0
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
1 0 2 0 1 0 1 0 0 2 2 2 2 2 0
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 u).
<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:
<lang j> +&* table 0 1 2 ┌───┬─────┐ │+&*│0 1 2│ ├───┼─────┤ │0 │0 1 1│ │1 │1 2 2│ │2 │1 2 2│ └───┴─────┘</lang>
percolate changes 1s in the first row to 2s, then flips over that result and performs an ooze right fold on suffixes, and then does that again (which restores the original orientation and propagates 2s in all directions). And it repeats this until all changes have been propagated.
<lang J> A 1 1 1 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1
(1 + # {. 1:) A
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
(* (1 + # {. 1:)) A
2 2 2 0 0 0 0 0 2 2 2 2 0 2 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 0 1 1
|. (* (1 + # {. 1:)) A
1 1 1 0 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 2 2 2 0 0 0 0 0 2 2 2 2 0 2 0
ooze/\. |. (* (1 + # {. 1:)) A
2 2 2 0 2 2 0 0 1 0 1 0 0 1 1 2 2 2 2 2 0 0 1 1 1 1 0 0 1 0 2 2 2 2 0 1 1 1 1 1 0 0 1 0 1 2 0 1 1 1 1 1 0 1 0 0 1 1 0 0 2 2 0 1 1 1 0 0 1 0 1 0 0 0 1 2 2 0 1 0 1 1 0 1 1 1 1 1 1 1 2 2 2 0 1 0 0 0 0 0 0 0 0 1 1 1 0 2 0 1 1 0 0 0 0 1 0 1 0 0 0 2 2 0 1 0 1 0 0 1 0 1 1 0 0 0 0 2 0 0 1 1 0 1 0 1 1 1 0 2 1 0 2 2 0 1 1 1 1 0 1 1 0 2 2 0 2 2 2 0 1 1 1 0 1 1 0 0 2 0 0 2 2 0 0 0 1 1 0 0 1 1 0 2 0 2 2 2 2 0 1 0 0 2 2 0 0 0 2 0 2 2 2 0 0 0 0 0 2 2 2 2 0 2 0
ooze/\.@|.^:2 (* (1 + # {. 1:)) A
2 2 2 0 0 0 0 0 2 2 2 2 0 2 0 2 2 2 2 0 1 0 0 2 2 0 0 0 2 0 0 2 2 0 0 0 1 1 0 0 1 1 0 2 0 0 2 2 2 0 1 1 1 0 1 1 0 0 2 0 1 0 2 2 0 1 1 1 1 0 1 1 0 2 2 0 0 2 0 0 1 1 0 1 0 1 1 1 0 2 0 2 2 0 1 0 1 0 0 1 0 1 1 0 0 2 0 2 0 1 1 0 0 0 0 1 0 1 0 0 2 2 2 0 1 0 0 0 0 0 0 0 0 1 1 2 2 0 2 0 2 2 0 1 1 1 1 1 1 1 2 2 0 2 2 2 0 0 1 0 1 0 0 0 1 2 0 2 2 2 2 2 0 1 0 0 1 1 0 0 2 2 2 2 0 1 1 1 1 1 0 0 1 0 1 2 2 2 2 2 0 0 1 1 1 1 0 0 1 0 2 2 2 0 2 2 0 0 1 0 1 0 0 1 1
ooze/\.@|.^:2^:2 (* (1 + # {. 1:)) A
2 2 2 0 0 0 0 0 2 2 2 2 0 2 0 2 2 2 2 0 1 0 0 2 2 0 0 0 2 0 0 2 2 0 0 0 1 1 0 0 1 1 0 2 0 0 2 2 2 0 1 1 1 0 1 1 0 0 2 0 1 0 2 2 0 1 1 1 1 0 1 1 0 2 2 0 0 2 0 0 1 1 0 1 0 1 1 1 0 2 0 2 2 0 1 0 1 0 0 1 0 1 1 0 0 2 0 2 0 1 1 0 0 0 0 1 0 1 0 0 2 2 2 0 1 0 0 0 0 0 0 0 0 2 2 2 2 0 2 0 2 2 0 2 2 2 2 2 2 2 2 2 0 2 2 2 0 0 2 0 1 0 0 0 1 2 0 2 2 2 2 2 0 2 0 0 1 1 0 0 2 2 2 2 0 2 2 2 2 2 0 0 1 0 1 2 2 2 2 2 0 0 2 2 2 2 0 0 1 0 2 2 2 0 2 2 0 0 2 0 2 0 0 1 1
ooze/\.@|.^:2^:3 (* (1 + # {. 1:)) A
2 2 2 0 0 0 0 0 2 2 2 2 0 2 0 2 2 2 2 0 1 0 0 2 2 0 0 0 2 0 0 2 2 0 0 0 1 1 0 0 1 1 0 2 0 0 2 2 2 0 1 1 1 0 1 1 0 0 2 0 1 0 2 2 0 1 1 1 1 0 1 1 0 2 2 0 0 2 0 0 1 1 0 1 0 1 1 1 0 2 0 2 2 0 1 0 1 0 0 1 0 1 1 0 0 2 0 2 0 1 1 0 0 0 0 1 0 1 0 0 2 2 2 0 1 0 0 0 0 0 0 0 0 2 2 2 2 0 2 0 2 2 0 2 2 2 2 2 2 2 2 2 0 2 2 2 0 0 2 0 2 0 0 0 2 2 0 2 2 2 2 2 0 2 0 0 1 1 0 0 2 2 2 2 0 2 2 2 2 2 0 0 1 0 1 2 2 2 2 2 0 0 2 2 2 2 0 0 1 0 2 2 2 0 2 2 0 0 2 0 2 0 0 1 1
ooze/\.@|.^:2^:_ (* (1 + # {. 1:)) A
2 2 2 0 0 0 0 0 2 2 2 2 0 2 0 2 2 2 2 0 1 0 0 2 2 0 0 0 2 0 0 2 2 0 0 0 1 1 0 0 1 1 0 2 0 0 2 2 2 0 1 1 1 0 1 1 0 0 2 0 1 0 2 2 0 1 1 1 1 0 1 1 0 2 2 0 0 2 0 0 1 1 0 1 0 1 1 1 0 2 0 2 2 0 1 0 1 0 0 1 0 1 1 0 0 2 0 2 0 1 1 0 0 0 0 1 0 1 0 0 2 2 2 0 1 0 0 0 0 0 0 0 0 2 2 2 2 0 2 0 2 2 0 2 2 2 2 2 2 2 2 2 0 2 2 2 0 0 2 0 2 0 0 0 2 2 0 2 2 2 2 2 0 2 0 0 1 1 0 0 2 2 2 2 0 2 2 2 2 2 0 0 1 0 1 2 2 2 2 2 0 0 2 2 2 2 0 0 1 0 2 2 2 0 2 2 0 0 2 0 2 0 0 1 1</lang>
(^:_ repeats an operation until it reaches a fixed point. In other words, it's basically a while loop.)
trial generates an arbitrary connection matrix and runs percolate on it. You'll typically get a different result from each trial.
<lang j> 0.6 0: 15 15 0
0.6 (] ?@$ 0:) 15 15 0.251168 0.233985 0.14541 0.219665 0.854985 0.0104645 0.449358 0.397573 0.0221767 0.701012 0.5692 0.320853 0.9029 0.0698325 0.439166 0.919973 0.31569 0.733443 0.397144 0.314414 0.0626569 0.125752 0.222472 0.859704 0.517682 0.249954 0.420026 0.974397 0.353249 0.199624 0.0632196 0.729989 0.0384723 0.962052 0.583483 0.794639 0.101726 0.987826 0.0711966 0.0199436 0.692024 0.281396 0.23614 0.445332 0.669898 0.817156 0.896721 0.128014 0.499834 0.86062 0.544871 0.296865 0.762644 0.583945 0.325163 0.701976 0.863764 0.631463 0.590224 0.0233733 0.577801 0.607615 0.893612 0.372065 0.692356 0.385318 0.948463 0.179848 0.482163 0.40125 0.690535 0.48328 0.936104 0.813984 0.319394 0.311636 0.27107 0.565229 0.152493 0.990904 0.856595 0.0755649 0.511731 0.636254 0.0199192 0.0299945 0.465337 0.472827 0.978434 0.207082 0.343524 0.388673 0.169093 0.133254 0.520914 0.736237 0.663096 0.757243 0.901397 0.367862 0.94831 0.45684 0.0569871 0.0211516 0.833437 0.745867 0.62734 0.790395 0.909088 0.359723 0.265804 0.176521 0.34355 0.0484308 0.775815 0.593603 0.023714 0.359704 0.621523 0.567126 0.866712 0.572275 0.679043 0.27958 0.649579 0.91871 0.229361 0.495236 0.646061 0.980648 0.563149 0.461033 0.630641 0.115773 0.460841
0.00359967 0.198523 0.509623 0.995623 0.395574 0.130878 0.458647 0.304251 0.552992 0.491661 0.0503197 0.523992 0.554198 0.818936 0.392742
0.696368 0.3988 0.931908 0.776482 0.23695 0.686757 0.799919 0.471909 0.441598 0.145376 0.470236 0.728451 0.567937 0.26908 0.564895 0.826714 0.202945 0.673436 0.655122 0.61951 0.0459954 0.777457 0.968675 0.418669 0.862087 0.836782 0.274477 0.483467 0.345968 0.530893 0.294519 0.286444 0.522912 0.455377 0.0480425 0.789532 0.22362 0.116726 0.563241 0.107526 0.000663275 0.36509 0.140703 0.694587 0.533685 0.155445 0.320069 0.102258 0.844235 0.981544 0.306235 0.627662 0.638738 0.806254 0.753405 0.391762 0.201705 0.07424 0.707749 0.373488 0.58236 0.384308 0.636697 0.577945 0.953101 0.527706 0.992441 0.242658 0.514722 0.269795 0.621798 0.528643 0.0910917 0.072488 0.746536 0.6 ([ >: ] ?@$ 0:) 15 15
1 1 0 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 1 0
0.6 ([ >: ] ?@$ 0:) 15 15
0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 0 1 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>
simulate runs a sequence of 15 by 15 trials and averages them. Since each trial is different, each run of simulate is different.
<lang j> 40 (%@[ * [: +/ (2 e. {:)@trial&15 15"0@#) 0.5 0.1
40 ((2 e. {:)@trial&15 15"0@#) 0.5
0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0
40 ((2 e. {:)@trial&15 15"0@#) 0.5
0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0
40 ([: +/ (2 e. {:)@trial&15 15"0@#) 0.5
6
40 ([: +/ (2 e. {:)@trial&15 15"0@#) 0.5
4
40 (%@[ * [: +/ (2 e. {:)@trial&15 15"0@#) 0.5
0.1
40 (%@[ * [: +/ (2 e. {:)@trial&15 15"0@#) 0.5
0.125</lang>
Note that the alternative implementation is different. (For example, there, percolate generates an arbitrary 15 by 15 connection matrix, and finds connections on that - rather like trial in this implementation.)