# Substitution tilings with parallelograms

I'm looking for a substitution tiling made with parallelograms, that is, a tiling of the plane with parallelograms (which do not have to be of the same shape) such that we can take one parallelogram and replicate the tiling inside it in a smaller scale.

I seek a decomposition of a given parallelogram into a set of smaller parallelograms that is not the obvious subdivision into four equal subparallelograms using midpoint subdivision.

I've searched the Tilings Encyclopedia with no luck. Does anyone know of such a tiling?

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if rhombus is ok you could skew a mathworld.wolfram.com/PerfectRectangle.html –  ryu jin Jan 11 '13 at 1:14