History
In 1973 and 1974, Roger Penrose discovered a family of aperiodic tilings, now called Penrose tilings. The first description was given in terms of 'matching rules' treating the prototiles as jigsaw puzzle pieces. The proof that copies of these prototiles can be put together to form a tiling of the plane, but cannot do so periodically, uses a construction that can be cast as a substitution tiling of the prototiles. In 1977 Robert Ammann discovered a number of sets of aperiodic prototiles, i.e., prototiles with matching rules forcing nonperiodic tilings; in particular, he rediscovered Penrose's first example. This work gave an impact to scientists working in crystallography, eventually leading to the discovery of quasicrystals. In turn, the interest in quasicrystals led to the discovery of several well-ordered aperiodic tilings. Many of them can be easily described as substitution tilings.
Read more about this topic: Substitution Tiling
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