Now a Harvard University researcher argues that more than 500 years ago, math whizzes met up with the artists and began creating far more complex tile patterns that culminated in what ...

But in each case these stars are surrounded by different shapes, which implies that the whole pattern never repeats in any direction. Therefore this graphic is an example of a pattern that has ...

Note: Image shows symmetric patterns (blue lines) constructed from decorated tiles (green, red and blue shapes); courtesy of W. B. Denny.