The interaction between rotation, gravity, and convection can cause planetary atmospheres to form patterns, as is seen in Saturn's hexagon and the Great Red Spot and stripes of Jupiter. The same processes cause ordered cloud formations on Earth, such as stripes and rolls. In the 1980s Lugiato and Lefever developed a model of light propagation in an optical cavity that results in pattern formation by the exploitation of nonlinear effects. Precipitating and solidifying materials can crystallize into intricate patterns, such as those seen in snowflakes and dendritic crystals. Mathematics Sphere packings and coverings. Mathematics underlies the other pattern formation mechanisms listed. Computer graphics Some types of automata have been used to generate organic-looking textures for more realistic shading of 3d objects. A popular Photoshop plugin, KPT 6, included a filter called 'KPT reaction'. Reaction produced reaction–diffusion style patterns based on the supplied seed image. A similar effect to the 'KPT reaction' can be achieved with convolution functions in digital image processing, with a little patience, by repeatedly sharpening and blurring an image in a graphics editor. If other filters are used, such as emboss or edge detection, different types of effects can be achieved. Computers are often used to simulate the biological, physical or chemical processes that lead to pattern formation, and they can display the results in a realistic way. Calculations using models like reaction–diffusion or MClone are based on the actual mathematical equations designed by the scientists to model the studied phenomena. References Bibliography External links SpiralZoom.com, an educational website about the science of pattern formation, spirals in nature, and spirals in the mythic imagination (archived 14 May 2019) '15-line Matlab code', A simple 15-line Matlab program to simulate 2D pattern formation for reaction-diffusion model. Developmental biology Articles containing video clips