What is a fractal simple definition?
A fractal is a non-regular geometric shape that has the same degree of non-regularity on all scales. Fractals can be thought of as never-ending patterns.
Who coined the term fractal?
This shape and structure, later known as the Mandelbrot set, was an extraordinarily complex and beautiful example of a “fractal” object, fractal being the name coined by Mandelbrot in 1975 to describe such repeating or self-similar mathematical patterns.
Is the golden ratio a fractal?
The Fibonacci Spiral, which is my key aesthetic focus of this project, is a simple logarithmic spiral based upon Fibonacci numbers, and the golden ratio, Φ. Because this spiral is logarithmic, the curve appears the same at every scale, and can thus be considered fractal.
Are our lungs fractals?
The lungs are an excellent example of a natural fractal organ. If you look at the tree upside-down (mouse over the image), you can see that the lungs share the same branching pattern as the trees. And it is for good reason! Both the trees and lungs have evolved to serve a similar function – respiration.
Are snowflakes fractals?
Part of the magic of snowflake crystals are that they are fractals, patterns formed from chaotic equations that contain self-similar patterns of complexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical copy of the whole in a reduced size.
What are three well known fractals?
Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals.
Why is pineapple a Fibonacci?
Pine. Pine comes from the root *peie meaning “to be fat, swell”. Could this relate to the Fibonacci spiral which grows you could even say it somewhat swells. The pineapple shows the fibonacci sequence as they possess the fibonacci spirals and also have the fibonacci sequence shown in the number of sections there are.
Why is cauliflower a Fibonacci?
The branched tips, called meristems, make up a logarithmic spiral, and the number of spirals on the head of Romanesco cauliflower is a Fibonacci number, which in turn is related to what’s known as the “golden ratio.”
Are rivers fractals?
Much like the circulatory system in the body, the planet Earth has fractal river networks that transport rainfall from the land to the oceans. Like all fractals, these complex, self-similar patterns are formed by the repetition of a simple process over and over.
Is lightning a fractal?
Similar to many shapes in nature, lightning strikes are fractals. A fractal is defined to be a rough or fragmented geometric shape that when magnified, is a reduced-size copy of the whole, a method known as self-similarity.
Is a tree a fractal?
Trees are fractal in nature, meaning that patterns created by the large structures, such as the main branches, repeat themselves in smaller structures, such as smaller branches.