Monday, 27 August 2012

Fractals - Order and Chaos

I have been fortunate to be given the space in a local gallery for a period of three weeks during which I will exhibit a set of images which are collectively known as Fractals. If you scroll to the bottom of this page you will see an example of the kind of images that will be on show. Fractals are often referred to as 'Geometry of Nature' because they seem to remind us of complex geometry of many structures in nature such as the coastline of an island or the cracks in weathered rock formations. Images such as these were popular in the 80s and the 90s, and many books with wonderful images were published.
For the exhibition it is necessary to write a short explanation of what these images represent and it is hard to find the words to explain the process without drowning the reader in complex mathematics and iterative equation manipulation programming techniques. In an attempt to make a start in assembling this write-up, here is what I have come up with...

The geometry of nature - Fractals - Order and Chaos
The images which makeup this exhibition have been generated by a computer program which follows the behavior of some mathematical equations that represent complex dynamics using complex variables. The behavior of these equations is represented by the images where the black regions are zones of stability and order and the brightly coloured areas are zones of chaos.
While mathematicians have known for hundreds of years that these equations behave chaotically, it is only in the last thirty years with the invention of computers and high resolution plotters that we are able to enjoy the chaotic behavior in glorious and beautiful images. The complex planes show self repeating patterns which seem to extend to specific boundaries which take us to the edge of the ordered zones.
When we view the images it is as if we are in the presence of something cosmic and familiar, and this is because many of the structures in nature and in our surroundings behave in a similar way. The coastline, the structures in biology and botany, the behavior of populations and economies, the meteorology, cosmology and the study of turbulence in air and fluids all have elements of chaos which is essentially what we can see in the images in this exhibition.

2 comments:

david stuart ryan said...



Arvinder

Striking picture and having as you say definite cosmic overtones.

David Ryan

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