Fibonacci Spiral in Nature
After I took the tulip leaf spiral shot that I posted yesterday, I wondered how closely it fit into the Fibonacci Spiral (which is mathematically related to the Golden Ratio). Here, I superimposed the Fibonacci Spiral onto the tulip leaf image (which I flipped horizontally) and also blended in a texture layer by Kim Klassen. While it's not an exact match, the approximation is certainly there.
Some people's eyes may glaze over with the details of following information, but for anyone wanting a tad more information about the Golden Ratio and the Fibonacci Spiral, here are some bits I collected from various places on the Internet:
The Golden Ratio was derived by the ancient Greeks and was used by them and the ancient Egyptians in the design of their buildings and monuments. They discovered that they could create a feeling of natural order, as well as structural integrity, in their works by applying the Golden Ratio. Artists since have used it for the same reason, to create a feeling of natural order in their works. At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.
The Fibonacci numbers are closely related to the Golden Ratio. By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, 13, and so on. The Fibonacci spiral superimposed on the leaf image above was created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling. The Fibonacci series overlayed on the leaf uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.
The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, daisies, sunflowers or the scales of a pineapple. Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem and some coniferous trees show these numbers in the bumps on their trunks. Palm trees show the numbers in the rings on their trunks. The Fibonacci numbers are applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even in the human body.
Most of the above material is from Wikipedia en.wikipedia.org/wiki/Fibonacci_number and
Fibonacci in Nature, by Nikhat Parveen jwilson.coe.uga.edu/emat6680/parveen/fib_nature.htm