<P> Water droplets fly off a wet, spinning ball in equiangular spirals </P> <P> In mathematics, a dynamical system is chaotic if it is (highly) sensitive to initial conditions (the so - called "butterfly effect"), which requires the mathematical properties of topological mixing and dense periodic orbits . </P> <P> Alongside fractals, chaos theory ranks as an essentially universal influence on patterns in nature . There is a relationship between chaos and fractals--the strange attractors in chaotic systems have a fractal dimension . Some cellular automata, simple sets of mathematical rules that generate patterns, have chaotic behaviour, notably Stephen Wolfram's Rule 30 . </P> <P> Vortex streets are zigzagging patterns of whirling vortices created by the unsteady separation of flow of a fluid, most often air or water, over obstructing objects . Smooth (laminar) flow starts to break up when the size of the obstruction or the velocity of the flow become large enough compared to the viscosity of the fluid . </P>

Types of patterns in mathematics in modern world