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
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.
Fascinating! A must watch!
Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series....
Check out the Custom Fibonacci Spiral Generator - chromatism.net