Patterns in nature

Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time. In the 19th century, the Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. The German biologist and artist Ernst Haeckel painted hundreds of marine organisms to emphasise their symmetry. Scottish biologist D'Arcy Thompson pioneered the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth. In the 20th century, the British mathematician Alan Turing predicted mechanisms of morphogenesis which give rise to patterns of spots and stripes. The Hungarian biologist Aristid Lindenmayer and the French American mathematician Benoît Mandelbrot showed how the mathematics of fractals could create plant growth patterns. Mathematics, physics and chemistry can explain patterns in nature at different levels and scales. Patterns in living things are explained by the biological processes of natural selection and sexual selection. Studies of pattern formation make use of computer models to simulate a wide range of patterns. Early Greek philosophers attempted to explain order in nature, anticipating modern concepts. Pythagoras (c. 570–c. 495 BC) explained patterns in nature like the harmonies of music as arising from number, which he took to be the basic constituent of existence. Empedocles (c. 494–c. 434 BC) to an extent anticipated Darwin's evolutionary explanation for the structures of organisms. Plato (c. 427–c. 347 BC) argued for the existence of natural universals. He considered these to consist of ideal forms (εἶδος eidos: "form") of which physical objects are never more than imperfect copies.