page_title: Patterns in nature
section_title: History
hierarchical_section_title: Patterns in nature / History
caption_attribution_description: English: male cone of Cycas circinalis in Olomouc (Czech Republic). Dansk: Hanlig kogle hos Falsk Sagocykas (Cycas circinalis), fotograferet i Olomouc, Tjekkiet Čeština: Cykas indický - samčí šiška ve skleníku v Olomouci
context_page_description: 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.
context_section_description: 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. Thus, a flower may be roughly circular, but it is never a perfect circle.
  Theophrastus (c. 372–c. 287 BC) noted that plants "that have flat leaves have them in a regular series"; Pliny the Elder (23–79 AD) noted their patterned circular arrangement. Centuries later, Leonardo da Vinci (1452–1519) noted the spiral arrangement of leaf patterns, that tree trunks gain successive rings as they age, and proposed a rule purportedly satisfied by the cross-sectional areas of tree-branches. Johannes Kepler (1571–1630) pointed out the presence of the Fibonacci sequence in nature, using it to explain the pentagonal form of some flowers. In 1754, Charles Bonnet observed that the spiral phyllotaxis of plants were frequently expressed in both clockwise and counter-clockwise golden ratio series. Mathematical observations of phyllotaxis followed with Karl Friedrich Schimper and his friend Alexander Braun's 1830 and 1830 work, respectively; Auguste Bravais and his brother Louis connected phyllotaxis ratios to the Fibonacci sequence in 1837, also noting its appearance in pinecones and pineapples. In his 1854 book, German psychologist Adolf Zeising explored the golden ratio expressed in the arrangement of plant parts, the skeletons of animals and the branching patterns of their veins and nerves, as well as in crystals. A. H. Church studied the patterns of phyllotaxis in his 1904 book. In 1917, D'Arcy Thompson published On Growth and Form; his description of phyllotaxis and the Fibonacci sequence, the mathematical relationships in the spiral growth patterns of plants showed that simple equations could describe the spiral growth patterns of animal horns and mollusc shells.
  In 1202, Leonardo Fibonacci introduced the Fibonacci sequence to the western world with his book Liber Abaci. Fibonacci presented a thought experiment on the growth of an idealized rabbit population.
  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. The discourse's central chapter features examples and observations of the quincunx in botany.
  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 studied soap films intensively, formulating Plateau's laws which describe the structures formed by films in foams.
  Ernst Haeckel (1834–1919) painted beautiful illustrations of marine organisms, in particular Radiolaria, emphasising their symmetry to support his faux-Darwinian theories of evolution.
  The American photographer Wilson Bentley took the first micrograph of a snowflake in 1885.
  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. He predicted oscillating chemical reactions, in particular the Belousov–Zhabotinsky reaction. These activator-inhibitor mechanisms can, Turing suggested, generate patterns (dubbed "Turing patterns") of stripes and spots in animals, and contribute to the spiral patterns seen in plant phyllotaxis.
  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 o
caption: Fibonacci number patterns occur widely in plant structures, including this cone of queen sago, Cycas circinalis
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