Fractals

I have decided to create my own fractal gallery, in which I will include the most interesting fractals I find. I will update it on whim, but check it every day in case there are more. For those of you who may not know what fractals are, read about them here. Some people create beautiful fractals, some are found in nature, and some may even be found accidentally.

Experiments on the effects of high voltage on various items has created some very interesting patterns in acrylic blocks, artificial lightning branching and distributing itself throughout the crystalline acryl.  In addition, separating acryl from a surface to which it was artificially bonded can create a fine, intricate "scar pattern" on the acryl or bonded surface. Novelties like this are now commonly and purposefully made, sold as novelty items. DVDs can also create fractal branching patterns when they are microwaved, as many children find out nowadays.

Many people create fractals on purpose, whether for personal enjoyment or scientific research. Benoit Mandelbrot, a Polish Jew that immigrated to France when he was a child, and then later in his life here to the US, created the Mandelbrot set, a fractal pattern which is arguably the most famous one ever created. There are three common ways to generate fractals:

1. Escape-time method: As defined by Wikipedia, "These are defined by a recurrence relation at each point in a space (such as the complex plane)."  The Mandelbrot set is one of these fractals, and many other famous fractals, such as the Julia set or the Burning Ship set, are also made using this technique.

2. Iterated function systems: These are fractals that have a pre-set placement rule, so while they may be infinite in detail, they cannot have the random patterns that make the other two methods so popular. A common example of this is the Cantor set, in which the a line is divided into thirds, and the third in the middle is taken away. The two resulting lines are then divided into thirds, the middles of which are taken away, and so on. Another example is the Infinite Pyramid, in which a triangle is continually subdivided using other triangles, all of which only differ in size.

3. Random fractals: The name says it all. Using computer programming designed to create random growth patterns of shapes, random fractals include fractal landscapes, fractal trees (including the famous Brownian Tree Program and Brownian Hierarchy), fractal molds, fractal explosions, and other such things that occur at least somewhat randomly in nature.

Fractals can also be found in nature. More obvious examples of this may include mountain snowflakes, clouds, bodily systems (namely the blood vessel network), plants, etc. One of the finest examples of this is the elegant Romanesco broccoli, which may appear soft and fluffy ( !) at first due to the infinite appearance of the detail and extension of its stubby fruit. Another, more common example of the fractal in nature is a fern, which like the Romanesco broccoli is not truly infinite in detail, still counts as a fractal in all respects. Fractals may appear in liquids as other compatible liquids are introduced. Sunflower heads also reflect a vague trend towards becoming fractals, although, on closer examination, it is apparent that they are only fractal-like for a very short range of magnification.