Penrose tilings are famous for being aperiodic: no finite translation can reproduce the same infinite tiling. However a common recursive method of generating Penrose tilings is periodic in the recursion iteration.

The recursive process approaches the pPnrose tiling as a tiling of two types of half-rhombs. In each iteration step, these triangles are subdivided into smaller ones, decreasing scale by a factor of 1/φ. 4 iterations produce a new tiling which includes the original.

This visualization animates the subdivision process with a continually increasing scale. After 4 interations and appropriate scaling, the original tiling reappears.

t is the time within the periodic loop and tau is the period length,