The Fibonacci Sequence in Nature





The fibonacci spiral appears not only in the perfect nautilus shell,  (image)





but in events and objects viewed from a far. An energy system in the shape of a fibonacci moves with limited losses. Hurricane Irene. imgur.com





The fibonacci as some of the largest structures in the universe. Spiral galaxies are the most common galaxy shape. Galaxies group together in superclusters and superclusters group together in walls. Currently the largest known structures are these walls or filaments of numerous superclusters that are gravitationally bound and separated by large areas of void. The Milky Way's dust obstructs us from seeing the depth of these filaments or sheets, so we do not yet know the exact shape of these walls. www.spacetelescope.org





The fibonacci appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner. Here, a microscopic view of the ovary of an Anglerfish. Nikon's It's a Small World Competition. www.dailymail.co.uk





Cancer cell division. This composite confocal micrograph uses time-lapse microscopy to show a cancer cell (HeLa) undergoing cell division (mitosis). The DNA is shown in red, and the cell membrane is shown in cyan. The round cell in the centre has a diameter of 20 microns. Credit Kuan-Chung Su, LRI, www.wellcomeimageawards.org

The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is a recursive sequence,  generated by adding the two previous numbers in the sequence.: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987...





If you were to draw a line starting in the right bottom corner of a golden rectangle within the first square, and then touch each succeeding multiple square's outside corners, you would create a fibonacci spiral.





Fibonacci as starting point of life. Image: www.holistichouseplans.com





Romanesque brocolli is a striking example of the fibonacci. www.flickr.com





Spiral aloe. Numerous cactus display the fobonacci spiral. www.flickr.com











Sunflower. www.thestrong.org





Marlborough Rock Daisy by Sid Mosdell. www.flickr.com





All pinecones display a fibonacci sequence.




American giant millipede. The fibonacci is thought to be the design of least resistence. Image by Alan Cressler. www.flickr.com




A monarch caterpillar about to form a chrysalis. natureremains.blogspot.com





Fibonacci and armor = very safe. www.fieldherpforum.com





Fibonacci in spores. A fiddlehead or koru. Photo by Sid Mosdell. www.flickr.com




Snails and fingerprints. Images: artcatalyst.blogspot.com, www.123rf.com





Fibonacci in the wave. artcatalyst.blogspot.com





Water falls into the shapes of a fibonacci during numerous events. Another example would be a vortex. fibonacci-seri.es





One blogger has applied the fibonacci sequence to population density and land mass. In Africa the majority of highly populated cities fall on or close to where the spiral predicts. earelephant.blogspot.com





Shell Fossil via: www.123rf.com



The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci (named after, he did not discover). Fibonacci's sequence was first introduced to the western world in 1202 by Fibonacci, the sequence had been noted by Indian mathematicians as early as the sixth century.*

The fibonacci also defines how the density of branches increases up a tree trunk, the arrangement of leaves on a stem, and how a pine cone's scales are arranged. Yet you will not see the fibonacci everywhere, as nature has many different methods and shades of survival.

Check out the Custom Fibonacci Spiral Generator - chromatism.net

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Lauren Domenia
Posts: 5

Awesome!!!
Reply #5 on : Wed May 08, 2013, 16:07:09

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another example of the glory and wonder of our God! That is simply amazing... I don't know what else to say!

C. Duane
Posts: 5

writings by Jay Hambidge
Reply #4 on : Sat February 23, 2013, 07:32:10

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http://books.google.com/books?ei=h7koUdOFMYyq0AHG14CYBA&id=Qq4gAAAAMAAJ&dq=jay+hambidge&jtp=12

http://books.google.com/books?ei=h7koUdOFMYyq0AHG14CYBA&id=Qq4gAAAAMAAJ&dq=jay+hambidge&jtp=17
(note reference to eleventh proposition of the second book of Euclid)

Jay Hambidge in the 1920s described "Dynamic Symmetry" and the "Whirling Square" being found in the Greek vase, the Parthenon, and in nature (like the shell and the sunflower head). The Dover reprint cover has an unfortunate, misleading illustration of static symmetry.

???
Posts: 5

fibbinocci
Reply #3 on : Wed January 23, 2013, 10:24:36

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thank you i need this for a science fair your pictures are awesome

Robin Mehdee
Posts: 5

Re: The Fibonacci Sequence in Nature
Reply #2 on : Sun December 16, 2012, 05:19:33

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Good job

kristin ramsden
Posts: 5

wonder
Reply #1 on : Thu December 13, 2012, 23:53:14

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marvel-ous!