Mathematics Can be Found in Nature

April 20, 2009 by uphaa

A fractal is generally “a rough or fragmented geometric shape that can be split into parts, each of which is at least approximately a reduced-size copy of the whole,”

A property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning “broken” or “fractured.” A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion

Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. .

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Aerial Photo Route Chicago to Houston.

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Water seeping from the sand at low tide created these amazing channels

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The chambers of a nautilus shell are an example of the Fibonacci spiral.

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Another interesting nature fractal is romanesco cauliflower, which is a cross between broccoli and Cauliflower, which accentuates the great fractal spiral patterns on the top.

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A picture of a spiral aloe, taken at the San Francisco Botanical Garden.

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Ice crystals growing on the ceiling of the underground garage, Antarctica, 2005

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Here is explained why Fibonacci numbers and the related number
ϕ are employed in nature. Their occurrence is not random or arbitrary. It is so because it must be so.
The sunflower, shown on the right, is a perfect example of the Fibonacci sequence and the corresponding “golden ratio” appearing in nature.

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Leaf Edges Sunlit

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Many flowers and plants follow the fractal or Fibonacci sequence pasterns. The cactus ,for example are sometimes fractals and some flowers follow the Fibonacci sequence:

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The little sea urchin on top is quite unusual. It was discovered by a research vessel near New Caledonia at a depth of 1000 ft.