Wave function collapse

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Write the solution for Wave Function Collapse based on the Coding Challenge 171: Wave Function Collapse and create new map 8x8 tiles with fourth T-blocks with variously directions (┤ ┴ ┬ ├) or blank tiles (space).

Reference WFC explained and another WFC explained

J

Implementation:<lang J>tiles=: 0,(|.@|:)^:(i.4)0,1 1 1,:0 1 0 wfc=: Template:Adj=. y</lang>

Here, m is the list of tiles, and i represents an 8x8 list of indexes into that list, with _1 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.

adj indexes into i -- for each item in i, adj 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 i "wraps around" on all sides). And, allow lists the allowable tiles corresponding to each of those adj constraints.

To build allow we first matched the left side of each tile with the right side of each tile (cartesian product) forming horz and similarly matched the tops and bottoms of the tiles forming vert. Then we built id which selects only the tile itself (or all tiles, for i=_1), north which limits tiles based on the tile above it, and so on for west, east, and south.

Once we're set up, we drop into a loop: todo selects the unchosen tile locations, wavelists for each location the eligible tiles, and entropy counts how many tiles are eligible for each location -- E is the entropy for the unchosen locations, and min is the smallest value in E. ndx is a randomly picked index into i 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 ┌──────┬──────┬──────┬──────┬──────┐ │ │ │ # │ # │ # │ │ │# # # │ # # │# # # │# # │ │ │ # │ # │ │ # │ └──────┴──────┴──────┴──────┴──────┘

  1j1#"1 ' #'{~ tiles wfc 8 8
       #           #     #                 #   
     # #   # # #   # # # #   # # # # # #   # # 
       #     #     #     #     #     #     #   
 #           #                 #     #         

1. # # # # # # # # # # # # # # # # # # # # # # #

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1. # # # # # # # # # # # # # # # # # # #

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  1j1#"1 ' #'{~ tiles wfc 8 8
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1. # # # # # # # # # # # # # # # # # #

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           # #     # # # #   # # # # # #   # # 
             #     #     #           #     #   </lang>