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The Penrose model is a common pattern that you probably already saw in a number a places without even noticing.
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original.
For more examples go to http://www.woollythoughts.com and http://www.math.ucdavis.edu/~greg/floors.html
The second picture (floor tiles) is not a Penrose tiling ….
I was guessing maybe the second one was the FAIL part of math fail? Because it certainly is not a penrose tile.
The first one isnt a penrose tiling either, although it looks similar. Penrose tilings are 5 way symmetric, on the bath mat(?) it’s only 4 way. See: http://en.wikipedia.org/wiki/Penrose_tiling
There is also a nice film about how to construct Penrose tilings at https://www.vismath.eu/en/films/penrose-tesselation