First you need to know about the Mandelbrot set... a simple mathematical formula (That's right I'm talking maths). The Mandelbrot set was created / discovered over 35 years ago. We know it to be a "fractal" a type of shape that often shows complex detail that replicates itself forever. No matter how far you zoom into the formula new replicated detail is seen.
The Mandelbrot fractal however is 2D and flat. The 3D Mandelbulb story starts with a guy named Rudy Rucker, an American mathematician, computer scientist and science fiction author (and in fact one of the founders of the cyberpunk science-fiction movement). Around 20 years ago, along with other approaches, he first imagined the concept behind the potential 3D Mandelbulb, and also wrote a short story about the 3D Mandelbrot in 1987 entitled "As Above, So Below". Back then of course, the hardware was barely up to the task of rendering the 2D Mandelbrot, let alone a 3D version - which would require billions of calculations to see the results, making research in the area a painstaking process to say the least.
When computers did catch up the first 3D fractals created lacked the finite detail that 2D fractals showed. Simply replicating the standard 2D fractal formula, spinning it 360 degrees in the Z direction yeilded un-exciting results.
Another fractal explorer, computer programmer David Makin was the first to render a 3D Mandelbulb that showed the results everyone was searching for. These first images reminded me of a newborn plant, with leaves and roots shooting off in all directions.
With each new completed render the true organic natural beauty of these 3D fractals became apparent and just how much they looked like naturally occuring life-forms. These organic mathematical shapes can be seen all around us, from the tinyist seashell in a rock pool to the coastlines and beyond.
I feel special but at the same time humbled, like a creative kid in a psychedelic fantasy microcosm, viewing rare visuals that I can control. I can't help but think that these formulas could be what we need to create true A.I. in the not to distant future.
By now you're thinking I'd like to try this for myself. The good news is there is free software for you to download. While the learning curve differs in each package there is a huge community online that can provide help.
Static images of 3D Fractals are great but the animation videos below will simply amaze. These videos especially the HD versions can take days even weeks to produce due to the processing power needed to produce each frame.
A variety of fractal related links. Various sites that contain more technical related information, galleries, papers and resources.