LOGO Challenge 5 - Patch

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
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LOGO Challenge 5 - Patch

Can you construct elegant procedures that will draw the squares and triangles and then this basic unit for a family of 'floor coverings'?

Can you construct procedures for tiling patterns based on this set of tiles?

Others have called them patches. Can you see why?