I find I keep coming back to this application every time I learn of a new optimization technique!

This time, it's projection onto (non-)convex sets, e.g. the "difference map" algorithm which was previously used to solve Sudoku puzzles (which is of-course another problem amenable to Linear Programming).

Here's an animation of the solver for a 30x30 image (note this seems to be as large as I could make it, the tiling projection is memory intensive..) using 24 grayscale Smith tiles:

A slightly longer walk-through of the projections I used can be found here, and I've attached the source-code. See the full discussion here: https://community.wolfram.com/groups/-/m/t/2823307

Hope you find watching the algorithm trying to climb out of a local minimum as mesmerizing as I do!

Attachments:

difference-map-t...nb

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This is really cool! There is a chapter about something similar to this in a book called Opt Art that you might enjoy. The whole book is about creating art with linear optimization.

Thanks ! It is awesome. I managed to make it work. But my computer being slow I do not yet have any cool result to share.

I am glad to see that the hack I did for the rounding problems in the vector code is also working on your configuration. The tiles are well aligning.

Thanks for sharing.

With some changes to the notebook, the photo mosaic case can be supported:

• The topological constraints must be disabled
• A new constraint must be added to prevent a tile from being reused more than once on the whole picture.

If I can find some time, I’ll update the notebook to support this case too.

Amazing idea - and nicely done! It truly generates a piece of art! Thanks for sharing!

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