Hexagonal Triangular Grid Mosaic in Photoshop

I make a hexagonal grid in Photoshop from regular equilateral triangles.

I then extend the technique to demonstrate how to make a hexagonal (triangular) mosaic without the use of special plugins or anything more than the standard Photoshop square mosaic tile filter.

I plan to use these techniques in conjunction with the 17 Wallpaper Group Plane Symmetries of programs like Artlandia Symmetryworks, TileBuilder, or Xaos Terrazzo to make even more elaborate pieces.

More on the topic of Distorting Photoshop Filters Without Distorting the Underlying Image

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Shawn Hargreaves has an interesting approach to hexagonal mosaics: he makes a Photoshop displacement map that fools every pixel in a hexagonal region from getting its color from the same pixel. I prefer an area average to a single pixel sample - that way a fleck of noise can't influence a whole hexagon - but the results look pretty good, and I like the ingenuity of the idea.