Most people have heard something about fractals. There are many natural fractal shapes like clouds, trees, broccoli, etc. The most famous mathematical fractal is the Mandelbrot set.
This fractal is two-dimensional. When this was invented, computers were very weak and in those days it wasn't possible to render three-dimensional fractals. Nowadays, the computing power of CPUs is thousands of times better. It has opened up many new possibilities.
By the end of 2007, a small group of people from www.fractalforums.com decided to develop algorithms and software for rendering 3D fractals. At the beginning everyone tried to expand the Mandelbrot set to three dimensions. First results were amazing. They get shapes like this one:
Rendering of first images took a lot of time, and was very
difficult because the first programs didn't have any user interface. Fractals were rendered slice by slice, so programs needed gigabytes of memory. After development of Distance Estimation algorithms, rendering became faster and with less memory consumption. Please follow this link to learn the history of 3D fractals.
New types of 3D formulas were also discovered.