Fractals

Hi,

A computer-generated 'fern'

I have always been fascinated by the concept of fractals and golden ratios. (I will cover the Golden Ratio another time.) I think anybody who looks at living things and the physical landscape of nature cannot help but wonder how everything is repeated again and again ad infinitum.

Self similarity: if the whole frond is a single leaf, each leaflet, each sub-leaflet and sub-sub-leaflet is a repeat of the whole

It is only a matter of scale really. At each level of increasing detail, it always look the same. Mathematicians call this property 'self similarity', and it is a property shared by many living and non-living things in nature: from ferns to forests, coastlines to pine cones, galaxies to gastropods, particles of sand to mountains...

I am attaching a few websites you may want to look at and appreciate what I mean.

A documentary on fractal concepts that I would like to share with you is presented by Arthur C. Clarke, one of my favorite science-fiction authors (e.g 2001: A Space Odyssey. BTW, he also invented the non-fiction concept of geo-stationary satellites that enabled modern telecommunications). The title of his film is "Fractals, the Colours of Infinity".

In this he explains the Mandelbrot Set. It is one of the most beautiful and remarkable discoveries of mathematics. It is mind-bending to think that the Mandelbrot Set is a closed shape - like a circle or square is closed - but unlike most familiar shapes, its edge has an infinite length. In other words, if you started at one point and began to trace around its edge, you would never finish.

I've placed a sample Set at right. This small image does not do justice to the intricacies and beauty of the form, so click on it to see it in all its hi-res glory.

The documentary is also available in 6 parts on Youtube, which may be easier chunks to view.

Youtube 1st part
2nd part
3rd part
4th part
5th part
6th part

Enjoy!

The next question is: why does nature use fractals? The answer has something to do with the related topic of golden ratios, which will have to wait for another posting here.

Cheers,
Have a nice day.

Everyone who is on the same wavelength with me on this is my soul mate.