Abstract
The beauty of tulips has enchanted mankind for centuries. The striped variety has attracted particular attention for its intricate and unpredictable patterns. A good understanding of the mechanism driving the striped pattern formation of broken tulips has been missing since the 17th century. It has been known since 1928 that these patterned tulips suffer from a viral infection by the tulip breaking virus. Here, we present a mathematical model to understand how a virus infection of the petals can lead to stripes, thereby providing a possible explanation of a 350 year-old mystery. The model, which describes the viral inhibition of pigment expression (anthocyanins) and their interaction with viral reproduction, incorporates a pattern formation mechanism identified as an activator-substrate mechanism, similar to the well-known Turing instability, working together with Wolpert's positional information mechanism. The model is solved on a growing tulip petal-shaped domain, whereby we introduce a new method to describe the tulip petal growth explicitly. This work shows how a viral infection that inhibits pigment production can lead to beautiful tulip patterns.