The mathematics of movement can describe the behaviour of all types of organisms, from cancer cells to humans.

Geometric hallucinations are very common: people get them after taking drugs, following sensory deprivation, or even after rubbing their eyes. What can they tell us about how our brain works?

Why are drug induced hallucinations so compelling that they apparently provided much of the inspiration for early forms of abstract art? Researchers suggest that the answer hinges on an interplay between the mathematics of pattern formation and a mechanism that generates a sense of value and meaning.