fascinating fractals

branches fractals

I’m still obsessed with water and trees – can’t get enough of them, and even I thought I’d be getting tired of them by now.  Recently, I came across a possible explanation for this, which lies in the idea of fractals.  Fractals, put simply, are complex and never-ending patterns that repeat themselves over different scales – if you’d like a beautifully simple, illustrated, one-page explanation of them, go here.

There are two sorts of fractals – the mathematical and the natural kinds  The mathematical kind, which are pretty to look at but which I’m certainly not capable of explaining adequately, are created by calculating a simple equation thousands of times and feeding the equation back to itself in a never-ending feedback loop.  The natural kind don’t need any understanding of mathematics to appreciate and can be seen all around us – you can find them in the branching patterns of trees, clouds, lightning, snowflakes, canyons, and river confluences, or in spiral forms such as seashells, hurricanes and galaxies.  Basically, the building blocks of natural things are fractal patterns and the human body is no exception – our lungs, blood vessels, brains, kidneys, and so on all display fractal patterns, and even the receptor molecules on viruses and bacteria are fractal in design.

Perhaps because of this, we like to look at fractal patterns and find them aesthetically pleasing.  Richard Taylor of Oregon University, who is working on developing artificial retinal implants to bring back lost sight, compares the way the camera ‘sees’ with the way the eye sees.  The eye only sees clearly what’s directly in front of it, with peripheral vision being much fuzzier, and so we have to move our eyes continually, scanning small areas, in order to ensure that the area of interest to us falls directly on the part of the eye with the sharpest vision – the pin-sized fovea.  In short, the natural movement of our eyes is fractal.  In contrast to this, a camera captures everything in uniform detail all over the picture plane.  If someone was given a retinal implant that was based on how a camera works, they would not only be overwhelmed with visual data, they would also see – in Taylor’s words –  ‘a world devoid of stress-reducing beauty’.

Almost certainly because we’re ‘made’ of fractals, it turns out that they have a strongly stress-relieving effect on us and looking at mid-range (don’t ask!) fractals can reduce stress by up to 60%.  It’s been known for a while, for example, that people with trees outside their hospital windows heal more quickly than those without, but nobody really knew why. One explanation lies in fractals.  A lot of art and architecture also forms fractal patterns, notably Gothic and Baroque architecture and the paintings of Jackson Pollock, De Kooning, Hokusai, and Escher.  They’re also found in African designs, Hindu temples and, indeed, all sorts of other places where you might find satisfying and soothing design elements.

So it seems that my fascination with water patterns and tree branches almost certainly has a lot to do with their fractal construction and without my being conscious of it, taking these kinds of pictures probably does a lot to de-stress me. Hopefully,  they do something to de-stress whoever looks at them as well.  Here are a few very recent images displaying the fractal patterns of winter tree branches, both on their own and reflected in water.

branches fractals winter trees

water reflections trees ripples abstract fractal

water reflections branches abstract ripples fractals

tree sunset branches silhouette fractal abstract

If you want to know more about fractals and how they affect us………