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Escher's "Lizards" Tessellation

M.C. Escher was the master of transforming polygonal tessellations into non-polygonal works of art. Before moving any of the sliders, examine Escher’s "Lizards" tessellation below. How can one lizard be moved to the position of a neighbour. What shape is the tile formed from? This probably works best if you only click one box at a time.
Modified from original by Duke which can be found here More examples can be found here