QuasiCrystals are crystal structures that are non-repeating. They were thought to be a mathematical curiosity that did not appear in nature. But in 1982 Daniel Shechtman detected them in electron microscope images of a rapidly cooled metal alloy. He received much resistance including when Linus Pauling, a colossus of science and a double Nobel laureate, mounted a frightening “crusade” against him. After telling Shechtman to go back and read a crystallography textbook, the head of his research group asked him to leave for “bringing disgrace” on the team. “I felt rejected,” Shachtman said. As it turned out he was right and was awarded the Nobel Prize in Chemistry in October 2011.

Earlier in the 1970’s Sir Roger Penrose was playing around with Penrose Tiles.  This is Roger Penrose standing on a floor tiled with one of his patterns:

And earlier than that M. C. Escher was playing around with repeating and non-repeating tiles:

And still earlier than that medieval Islamic architects were adding these tiles to Mosques and other structures, using only 5 geometric shapes

All of these expressions have fascinated me for years.  Here are some of my favorites, one is more beautiful then the last one: