Fractal art is a marriage made in heaven - especially when you are an imaging scientist interested in beauty, philosophy, and spirituality!
Images from the Mandelbrot and Julia sets of fractals (see link for details of the mathematics)
What is a fractal?
Scientifically, a fractal is a never-ending pattern. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions.
Fractals are infinitely complex patterns that are “self-similar” across different scales. Imagine a tree - starting with the main stem, branching into the first set of branches, which continue to branch into thinner and finer branches, over and over again, through many, many generations. Similar is the “self-similarity” of the branches of our own respiratory system, our circulatory system, and our nervous system - to just name a few. So are the patterns of a lightning bolt or river networks, or dry, cracked earth!
If we look around us and pay attention to what we see, soon, we find that very few things in nature are self-contained and unique. If you will, we are all mirror reflections of each other. Not exact replicas, mind you, but “self-similar.”
Indeed, poets in all places and times have already intuited this truth.
The Tao begot one.
One begot two.
Two begot three.
And three begot the ten thousand things.
~ Tao Te Ching (translated by Gia-Fu Feng and Jane English; original from at least fourth century BCE, if not older )
And closer to our time and place, the nineteenth century English poet, William Blake, wrote:
To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour.
~ Auguries of Innocence by William Blake (published 1863; presumed to be have been written in 1803)
Thus, if you have a fractal pattern, you can zoom in deeper and deeper, to find the pattern repeated at smaller and smaller scales - although with some variation each time. The idea is very reminiscent of creation myths from cultures around the world - which all speak of some Primordial Being - in some cultures called God - who creates the world “of ten thousand things” - in their own image.
It is also reminiscent of the Hermetic dictum, “as above, so below.”