Many shapes and forms in nature can be thought to be completely unpredictable and chaos like. Yet viewed as a whole, they can create the most beautiful patterns. Inherent coding or beauty in chaos?
These patterns are known as fractals and defined as “a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole”. The term was coined by franco-american mathematician Benoit Mandelbrot in 1975 and is derived from the latin fractus meaning broken or fractured.
The main law fractals follows is called self-similarity. Self-similarity is mostly defined in mathematics. A self-similar object is (or practically is) similar to a smaller part of itself. Fractals can be divided into three different types:
– Exact self-similarity
– Statistical self-similarity
They usually have the following features:
– at small scales, they have a very fine structure
– they are too irregular to be defined by classical geometry
– they have varying levels of self-similarity
– they have a simple and recursive definition (they can be defined by a portion of themselves)
Apart from the obvious artistic interest in these patterns, fractals are used in a wide variety of fields. From classification in medical slides, to modeling landscapes through generating music, these beautiful patterns can enlighten our vision.
In the honour of Benoit Mandelbrot, who passes away on the 14th of October 2010, here are some breathtaking images.
|A wood stalk cross section|
|Seaweed and Coral|
|Mountains in Tibet|
|Natural Could Spirals|