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I want a method to tile arbitrary square image. For most cases the boundaries do not agree. So I are looking for a transformation from a square image to a square image whose boundaries agrees.

One way to formulate this problem is to find a "interesting" continuous map L : T -> [0,1]^2, where T is [0,1]^2 with identified boundaries.

Below is one such transformation. From a non-tile-able to a tile-able.

01transformed to-> 02

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