The most intricate crop circles, which have baffled experts and fuelled rumours of alien visitors, have relied upon careful planning and execution. In the past, the best crop circles have attracted ...

We prove existence and uniqueness results for patterns of circles with prescribed intersection angles on constant curvature surfaces. Our method is based on two new functionals--one for the Euclidean ...

Looking for a challenging and stimulating activity? Try solving a pattern-based puzzle posted on Instagram by Optical Illusions. The puzzle presents three patterns and asks you to predict the next ...

Patterns appearing on both the very large and very small scale are extremely rare, but researchers have found a similar pattern in two apparently unrelated systems -- skin cells and fairy circles in ...