WHAT IS A FRACTAL It’s a geometrical shape that divides up into parts that each appear to be a smaller copy of the whole, a process that can continue to infinity.
Mathematicians have long engaged in expressing this property of “self-similarity” through equations, but it was only in the 1970s that French-American practitioner Benoit Mandelbrot came up with the term “fractal” (from the Latin for broken).
It’s an area of considerable complexity, but fractals are found all over the place in nature – ever looked closely at a cauliflower and its florets, for example, or certain corals or sponges Scientists seem to find the theory useful, and so these days do artists, one of whom happens to be a French diver based in Marseille.
Francis Le Guen is a man of many parts, though they all seem to cross over. Now 50, he comes from an artistic family and started out as a photo-journalist and documentary film-maker, but he also writes for TV and has edited two French diving magazines. One way and another, the underwater world informs many of his activities.
As the part played by computer graphics in film-making became more important, Francis kept abreast of emerging techniques, which eventually led him to add “3D graphic designer” and “fractalist” to his CV.

AFTER DISCOVERING ALL THE EXOTIC software available to 21st century digital artists, packages with names such as Ultrafractal and Mandelbulb 3D, Francis started turning out work based, among other things, on his underwater photography.
“Its diving, and especially cave-diving, that first inspired me to make images,” he says. “I made my first photos in flooded caves. The underwater landscapes I discovered were so unreal – and I now realise that this was because they were fractal. Natural forms come under the laws of fractal mathematics.
“When I decided to make digital paintings I chose the underwater world, because its my world. I know the feeling, the texture of water, the way the light plays in the composition.
“And I discovered that the software could generate quite easily the underwater mood I love. There are other fractalists but no one, as far as I know, making underwater scenes.
“I’ve always explored,” he goes on.
“I practised scuba-diving and cave-diving for two decades at the highest level, discovering fabulous worlds.”
He reckons an explorer’s instincts are needed “to get lost in the jungle of algorithms” on which fractals are based.
By transforming the equations that govern natural structures into points in space, he explains, visual representations emerge that feature the same patterns at any scale.
Working with fractals in 3D became possible only with the emergence two years ago of Mandelbulbs. With the latest software, he says, “it is possible
to combine different fractals with each other and to explore in depth.” (Still with us Frankly, I’m struggling).
“These fractals give us a better understanding of the world around us,” he says. “I try to understand nature in its fractal dimensions. Often a detail catches my eyes that later becomes an illustration.
“The goal is not to reproduce reality but to create new parallel worlds with other organic rules. A small variation in the initial parameters can cause a ‘butterfly effect’ and completely change the appearance of the created world.
“The trick is to try to steer the chaos. Given the complexity of the tools, this means learning to sculpt water!”

IT ALL STARTS WITH a general idea of the scene and atmosphere. “Depending on what’s wanted, we combine various changes and get a ‘world’.
“Then the exploration begins.
I navigate inside the fractal to appreciate its possibilities – the correct ways, and how to generate variations.
“Then it’s the tasks of a photographer or director: I choose the angle, the focal depth of field, set the lighting, shadows, effects and camera movements. Then comes the final stage of rendering.
“Each stage of the process may require days of development and often the goal is never achieved! Detailed as it is, the 3D world has its limits, but with fractals, it’s endless. The level of detail increases as you approach, and new worlds go on appearing.”
Francis Le Guen is currently working on an interactive 4D book or tablet in which the reader will be able to navigate within the images, and foresees the making of an underwater fractal movie.
In the meantime, back at good old 2D level, you can buy posters, prints and greetings cards featuring his fractal designs through his company Artflakes, www.artflakes.com.