Causesįor more details, see Symmetry in biology In 1975, after centuries of slow development of the mathematics of patterns by Gottfried Leibniz, Georg Cantor, Helge von Koch, Wacław Sierpiński and others, Benoît Mandelbrot wrote a famous paper, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, crystallising mathematical thought into the concept of the fractal. L-systems have an alphabet of symbols that can be combined using production rules to build larger strings of symbols, and a mechanism for translating the generated strings into geometric structures. In 1968, the Hungarian theoretical biologist Aristid Lindenmayer (1925–1989) developed the L-system, a formal grammar which can be used to model plant growth patterns in the style of fractals. These activator-inhibitor mechanisms can, Turing suggested, generate patterns of stripes and spots in animals, and contribute to the spiral patterns seen in plant phyllotaxis. He predicted oscillating chemical reactions, in particular the Belousov–Zhabotinsky reaction. In 1952, Alan Turing (1912–1954), better known for his work on computing and codebreaking, wrote The Chemical Basis of Morphogenesis, an analysis of the mechanisms that would be needed to create patterns in living organisms, in the process called morphogenesis. The American photographer Wilson Bentley (1865–1931) took the first micrograph of a snowflake in 1885.ĭ'Arcy Thompson pioneered the study of growth and form in his 1917 book The German psychologist Adolf Zeising (1810–1876) claimed that the golden ratio was expressed in the arrangement of plant parts, in the skeletons of animals and the branching patterns of their veins and nerves, as well as in the geometry of crystals.Įrnst Haeckel (1834–1919) painted beautiful illustrations of marine organisms, in particular Radiolaria, emphasising their symmetry to support his faux- Darwinian theories of evolution. He studied soap films intensively, formulating Plateau's laws which describe the structures formed by films in foams. The Belgian physicist Joseph Plateau (1801–1883) formulated the mathematical problem of the existence of a minimal surface with a given boundary, which is now named after him. He showed that simple equations could describe all the apparently complex spiral growth patterns of animal horns and mollusc shells. His description of phyllotaxis and the Fibonacci sequence, the mathematical relationships in the spiral growth patterns of plants, is classic. In 1917, D'Arcy Wentworth Thompson (1860–1948) published his book On Growth and Form. The discourse's central chapter features examples and observations of the quincunx in botany. In 1658, the English physician and philosopher Sir Thomas Browne discussed "how Nature Geometrizeth" in The Garden of Cyrus, citing Pythagorean numerology involving the number 5, and the Platonic form of the quincunx pattern. Fibonacci gave an (unrealistic) biological example, on the growth in numbers of a theoretical rabbit population. 1250) introduced the Fibonacci number sequence to the western world with his book Liber Abaci. Studies of pattern formation make use of computer models to simulate a wide range of patterns. Patterns in living things are explained by the biological processes of natural selection and sexual selection. Mathematics, physics and chemistry can explain patterns in nature at different levels. Hungarian biologist Aristid Lindenmayer and French American mathematician Benoît Mandelbrot showed how the mathematics of fractals could create plant growth patterns. In the 20th century, British mathematician Alan Turing predicted mechanisms of morphogenesis which give rise to patterns of spots and stripes. ![]() Scottish biologist D'Arcy Thompson pioneered the study of growth patterns in both plants and animals, showing that simple equations could explain spiral growth. German biologist and artist Ernst Haeckel painted hundreds of marine organisms to emphasise their symmetry. ![]() In the 19th century, Belgian physicist Joseph Plateau examined soap films, leading him to formulate the concept of a minimal surface. The modern understanding of visible patterns developed gradually over time. Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. These patterns recur in different contexts and can sometimes be modelled mathematically. Patterns in nature are visible regularities of form found in the natural world. Patterns of the veiled chameleon, Chamaeleo calyptratus, provide camouflage and signal mood as well as breeding condition.
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