## Sunday, June 29, 2008

### Fractal Oranges

I am too tired today to post about polynomials (because it requires to use latex for typing math formulas and a bit of drawing), so this is a post about fractals in every day life. I was sent an interesting example of such fractal by a friend, and I thought to post about it here. Look on the following photos:

This is the "fractal stage"

The final product

And this is how it all started.

You probably wonder how it is connected to fractals. The answer is simple - the process in which this orange was made is iquivalent to creating a fractal. We took a symmetrical complex shape (the third photo) and then we squished it without loosing the symmetry. The result (the first photo) is in fact the original one, in many copies. We will need to slice it, but if we will do it, we will get a lot of smaller copies of the original shape. Which means we can repeat the process again and again. Now if we will look on this process in four dimensional space (with time as the fourth dimension), it is obvious that the result is a fractal. The more we "zoom in" (zooming is going forward in time) the more our figure becomes complex and with smaller details. However, it always resemble the original shape. Thus, by definition this is a fractal. You can find more photos here.