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Further stress in the same direction would then simply open the existing cracks; stress at right angles can create new cracks, at 90 degrees to the old ones.

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Thus the pattern of cracks indicates whether the material is elastic or not. Since each species of tree has its own structure at the levels of cell and of molecules, each has its own pattern of splitting in its bark. Cooled basalt at Giant's Causeway. Leopards and ladybirds are spotted; angelfish and zebras are striped.

One function of animal patterns is camouflage ; [25] for instance, a leopard that is harder to see catches more prey. Another function is signalling [26] — for instance, a ladybird is less likely to be attacked by predatory birds that hunt by sight, if it has bold warning colours, and is also distastefully bitter or poisonous , or mimics other distasteful insects. A young bird may see a warning patterned insect like a ladybird and try to eat it, but it will only do this once; very soon it will spit out the bitter insect; the other ladybirds in the area will remain undisturbed. The young leopards and ladybirds, inheriting genes that somehow create spottedness, survive.

But while these evolutionary and functional arguments explain why these animals need their patterns, they do not explain how the patterns are formed. Dirce beauty butterfly, Colobura dirce. Grevy's zebra , Equus grevyi. Royal angelfish , Pygoplites diacanthus.

Sacred Geometry: Mathematical Patterns Behind Nature, Body, Mind, and Spirit

Array of ladybirds by G. Breeding pattern of cuttlefish , Sepia officinalis. Alan Turing, [16] and later the mathematical biologist James Murray , [80] described a mechanism that spontaneously creates spotted or striped patterns: a reaction-diffusion system. If the morphogen is present everywhere, the result is an even pigmentation, as in a black leopard.


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But if it is unevenly distributed, spots or stripes can result. Turing suggested that there could be feedback control of the production of the morphogen itself. This could cause continuous fluctuations in the amount of morphogen as it diffused around the body. A second mechanism is needed to create standing wave patterns to result in spots or stripes : an inhibitor chemical that switches off production of the morphogen, and that itself diffuses through the body more quickly than the morphogen, resulting in an activator-inhibitor scheme. The Belousov—Zhabotinsky reaction is a non-biological example of this kind of scheme, a chemical oscillator.

Later research has managed to create convincing models of patterns as diverse as zebra stripes, giraffe blotches, jaguar spots medium-dark patches surrounded by dark broken rings and ladybird shell patterns different geometrical layouts of spots and stripes, see illustrations. These require an oscillation created by two inhibiting signals, with interactions in both space and time. Patterns can form for other reasons in the vegetated landscape of tiger bush [85] and fir waves. Each roughly horizontal stripe of vegetation effectively collects the rainwater from the bare zone immediately above it.

When trees fall, the trees that they had sheltered become exposed and are in turn more likely to be damaged, so gaps tend to expand downwind. Meanwhile, on the windward side, young trees grow, protected by the wind shadow of the remaining tall trees. In permafrost soils with an active upper layer subject to annual freeze and thaw, patterned ground can form, creating circles, nets, ice wedge polygons, steps, and stripes. Thermal contraction causes shrinkage cracks to form; in a thaw, water fills the cracks, expanding to form ice when next frozen, and widening the cracks into wedges.

These cracks may join up to form polygons and other shapes. The fissured pattern that develops on vertebrate brains are caused by a physical process of constrained expansion dependent on two geometric parameters: relative tangential cortical expansion and relative thickness of the cortex. Similar patterns of gyri peaks and sulci troughs have been demonstrated in models of the brain starting from smooth, layered gels, with the patterns caused by compressive mechanical forces resulting from the expansion of the outer layer representing the cortex after the addition of a solvent.

Numerical models in computer simulations support natural and experimental observations that the surface folding patterns increase in larger brains. Giant pufferfish , Tetraodon mbu. Snapshot of simulation of Belousov-Zhabotinsky reaction. Helmeted guineafowl, Numida meleagris , feathers transition from barred to spotted, both in-feather and across the bird.

Aerial view of a tiger bush plateau in Niger. Fir waves in White Mountains , New Hampshire. Patterned ground : a melting pingo with surrounding ice wedge polygons near Tuktoyaktuk , Canada. Fairy circles in the Marienflusstal area in Namibia. Human brain superior view exhibiting patterns of gyri and sulci. From Wikipedia, the free encyclopedia. Visible regularity of form found in the natural world.

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The Fractal Geometry of Nature

Further information: Symmetry in biology , Floral symmetry , and Crystal symmetry. Garnet showing rhombic dodecahedral crystal habit. Volvox has spherical symmetry. Branching pattern of a baobab tree. Further information: phyllotaxis. Fibonacci spiral. Bighorn sheep , Ovis canadensis. Meanders: sinuous path of Rio Cauto , Cuba.

Decoding the Secret Patterns of Nature - Fibonacci Ratio & Pi - Full Documentary

Dunes: barchan crescent sand dune. Main article: tessellation. Palm trunk with branching vertical cracks and horizontal leaf scars. Leopard , Panthera pardus pardus. Main article: Pattern formation. Aristotle , Metaphysics 1—5 , c. Stanford Encyclopedia of Philosophy. Retrieved 4 May New York City: Broadway Books. Taylor, Pamela ed.


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The Notebooks of Leonardo da Vinci. New American Library. Proportion: Science, Philosophy, Architecture. Nexus Network Journal. D' Arcy University of Dundee and the University of St Andrews. Retrieved 16 October Acharya Hemachandra and the so called Fibonacci Numbers. Siwan, 20 1 —30, How Nature Geometrizeth. The Garden of Cyrus. Encyclopedia of Nineteenth-Century Photography. CRC Press. Philosophical Transactions of the Royal Society B.

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The Mathematical Theory of L Systems. Academic Press , New York, The fractal geometry of nature.


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