Is it it real or is it imaginary?

Most of you will have heard about fractals.  These are real or mathematical systems that exhibit a phenomenon called “self-similarity”.  That means that they have a detailed pattern that repeats itself.  The most extreme systems, such as the Mandelbrot Set, have such a degree of pattern repeating that it’s almost impossible to determine at what scale you are observing the system.

Here’s an example of a computer-generated fractal that produces a structure very similar to the leaf of a fern.  You can see that each leaf is the same as the larger structure, and so on down to the parts of the leaves. To generate it I used free software called ChaosPro.

“Fractal Fern” by Derek Gale

You can see that it is remarkably similar to a fern.  I looked in the garden for, not a fern, but another plant that had some degree of self-similarity. I found one very quickly, so I took a nice simple shot with my Sigma 50mm macro lens.  It was, of course, a bit more complicated than that as it was windy, so I had to wait for a quiet moment.  It was also quite sunny so I needed a flower in the shade to keep the contrast down.  That still, shady flower needed to have the right background which was far enough away to render out of focus.

“Fractal flower” by Derek Gale

The plant I found was a crocosmia with a not-fully-open flower .  You can see that the overall shape is much the same as the fractal fern, and that the buds repeat as they get smaller.  You could define the shape of this flower with a mathematical equation and produce it on the computer, although one thing that you won’t get on a computer generated fractal is a cobweb!

Isn’t it great when maths and nature work together?!

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