About Fractals


I have been cottaging for a couple of weeks with our family. I’m really enjoying the ease of summer, the sunny mornings where all the wet towels (which spend the night in the screened porch) are hung outside to dry and freshen up in the sun before the day’s events. Ah the sun – how would we ever manage without it!

I’m nurturing an interest in fractals, trying to understand them better, and see them more readily both in nature and eventually elsewhere in the built environment. I take my paddleboard out in the early mornings to explore the trees along the banks where the fractals are numerous and diverse – once you develop the eye for them. My interest in fractals stems from a broader interest in complex adaptive systems, and how an understanding of CAS can help us to better understand and adapt to changes in our organizational structures and activities, our relationships, even the ups and downs of family life.

There are many interesting definitions, and excellent photographs, of fractals on the web. I’ve tried in this post to pull out some of the simplest, most informative and easy to understand ones – so that I can find them more readily.

A fractal is a never-ending pattern, an infinitely complex geometric arrangement that is self-similar across different scales. Fractals are created by repeating a simple process over and over in an ongoing feedback loop. “Driven by recursion, fractals are images of dynamic systems.” Fractal patterns are extremely familiar, since nature is full of them. Trees, rivers, coastlines, mountains, clouds, seashells, hurricanes are just some of the fractal patterns seen frequently in nature.

Abstract fractals – such as the Mandelbrot Set – can be generated by a computer repeatedly calculating a simple equation over and over. In mathematics a fractal is an abstract object used to describe and simulate naturally occurring objects. Fractals are geometric figures (says one website) each part of which has the same statistical character as the whole, and in which similar patterns recur at progressively smaller scale. Fractals are useful in describing seemingly random phenomena such as crystal growth and galaxy formation. They are useful in modelling structures such as eroded coastlines or snowflakes.

Early research (see for example The Nature Fix by Florence Williams) indicates that seeing and appreciating nature’s fractals is good for the human brain. Falma writes in her blog: ”I remember how much more beautiful the sight of bare tree branches against a grey November sky became to me once I had learned to see them in terms of fractals”

My favourite personal fractal photo.

Next challenge – and the next post – will explore the connections between fractals and complexity.

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