Inroducing Fractal Geometry / The Fractal Geometry of Nature

I picked this up out of interest when I was looking at the Edinburgh Central Library as a collection, it turns out it's more than relevant to what I've been looking at. 'The Fractal Geometry of Nature' hurt my brain a bit at first so I have to admit I started of with 'Introducing Fractal Geometry'. In a wider sense it was incredible thinking about the relevance of the concept of fractals in general. I don't want to spend a lot of time talking about all the different ways that fractal measurements are used, but rather focus on it relevance in context of my chosen subject.

The point of fractals is that they can be used to understand even forms and measurements which appear incredibly random, like coastlines, blood cells and cloud formations.

Through ideas of self-similarity - which theorists like Koch and Sierpinski had already laid the foundations for - Mandelbrot discovered patterns in the most amorphous corners of nature. As a result fractals measurements are now at the forefront of Cancer research and cures for diseases like AIDS*. I'm going to continue reading this in an attempt to better understand the techniques he uses, but in terms of the time constraint of the project, I'd like to focus on the importance of the self-similarity side of things, by discovering patterns in nature, we gain a greater understanding of how it works. In a really, really basic overview; Mandelbrot found that although shapes varied in size and position they would maintain there original form. In terms of the importance of the regular shapes I've been looking at;

"The homogenous distribution on a line, plane, or space has two very desirable properties. It is invariant under displacement, and it is invariant under change of scale." (Mandelbrot, B, 1977)

*Lesmoir-Gordon, N., Rood, W., Edney, R. (2000) Introducing Fractal Geometry, Cambridge: Totem Books