Fractals are one of the most interesting puzzles of mathematics – they are based on simple formulas, yet produce beautiful and complex designs. There are many fractal shapes in nature such as clouds, trees, broccoli and snowflakes. The most famous mathematical fractal is the Mandelbrot set, named after the mathematician Benoît Mandelbrot (20 November 1924 – 14 October 2010), who studied and popularized it.
By the end of 2007, a small group of people from www.fractalforums.com decided to develop algorithms and software for rendering 3D fractals. These fractals can be zoomed infinitely like two-dimensional fractals, but since they form a virtual 3D space, it is possible to fly through the fractal.
This animation shows interior of Tglad’s Mandelbox fractal. It was rendered using Krzysztof Marczak’s program Mandelbulber, which can be downloaded from www.sourceforge.net/projects/mandelbulber/. You can check Krzysztof’s Deviantart gallery at krzysztofmarczak.deviantart.com/gallery/
Here are some images created by MarkJayBee on Deviantart, who has written the formulas for each, and links many tutorials on his page:
The mind boggles at the possibilities for an interactive and mindbending game using 3D Fractals! Combine Minecraft with Mandelbulber to make ‘Mandelcraft’ – exploring, mining and building mathematical structures! You could fly through an endlessly evolving 3D fractal formula as it morphs around you, opening and closing routes throughout the structure. Shooting craters and fragmenting the pattern would create ripples in the formula that would sweep across the entire structure, and you could land your ‘ship’ on vast mathematical landscapes to explore and interact with! Another idea would be to use Mandelbulber as a Homeworld 2 mod! Time to upgrade the PC and get started!