Wave function collapse: Difference between revisions
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Implementation:<lang J>tiles=: 0,(|.@|:)^:(i.4)0,1 1 1,:0 1 0
wfc=: {{
adj=. y#.y|"1(y#:,i.y)+"1/0,<:3 3#:1 3 5 7
horz=. ({."1 -:"1/ {:"1) m NB. horizontal tile pairs
vert=. ({."2 -:"1/ {:"2) m NB. vertical tile pairs
id=. <@I.(=i.#tiles),1 NB. identity constraint
north=. <@I.vert,1 NB. adj 1 constraint
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,/"2,/0 2 1 3|:(y$i){m
}}</lang>
Here, <code>m</code> is the list of tiles, and <code>i</code> represents an 8x8 list of indexes into that list, with <code>_1</code> being a placeholder for the case where the index hasn't been choosen -- initially, we pick a random location in i and assign an arbitrarily picked tile to that location.
<code>adj</code> indexes into <code>i</code> -- for each item in <code>i</code>, <code>adj</code> selects that item, the item "above" it, the item to the "left" of it, the item to the "right" of it and the item "below" it (with scare quotes because the tile represented by <code>i</code> "wraps around" on all sides). And, <code>allow</code> lists the allowable tiles corresponding to each of those <code>adj</code> constraints.
To build <code>allow</code> we first matched the left side of each tile with the right side of each tile (cartesian product) forming <code>horz</code> and similarly matched the tops and bottoms of the tiles forming <code>vert</code>. Then we built <code>id</code> which selects only the tile itself (or all tiles, for <code>i=_1</code>), <code>north</code> which limits tiles based on the tile above it, and so on for <code>west</code>, <code>east</code>, and <code>south</code>.
Once we're set up, we drop into a loop: <code>todo</todo> selects the unchosen tile locations, <code>wave</code>lists for each location the eligible tiles, and <code>entropy</code> counts how many are eligible for each location -- <code>E</code> is the entropy for the unchosen locations, and <code>min</code> is the smallest value in <code>E</code>. <code>ndx</code> is a randomly picked index into <code>i</code> with minimal entropy and for that location we randomly pick one of the options and update i with it. (When there's only one option remaining "randomly pick" here means we pick that option.)
Once we've assigned a tile to every location in i, we use those indices to assemble the result.
For task purposes here, we will use space to represent a white pixel and "#" to represent a black pixel. Also, because characters are narrow, we will insert a space between each of these "pixels" to better approximate a square aspect ratio.
Task example (the initial tiles and two runs of wave function collapse (two, to illustrate randomness):<lang J> (<"2) 1j1#"1 ' #'{~ tiles
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