Summer 2017, I worked on a group project with two other teammates as part of the Northwest Programming Workshop (NWAPW) to develop software capable of rendering the Mandelbulb fractal in realtime. In addition to studying the interesting mathematics, we were able to produce some truly beautiful images (a couple are below). The project is hosted on Github: https://github.com/Ibrahim9999/3D-Mandelbrot-Project. The program is written in C and uses OpenGL for most of the rendering and computation. Documentation is scarce, but anyone should be able to easily build it and see this magnificient fractal for themselves.
The mandelbulb is a 3D fractal. Similar to the famous "Mandelbrot Set", a 2D fractal graphed on the complex plane, the mandelbulb utilizes 3 dimensional complex numbers rather than the usual 2D complex numbers. In order to display the 3D fractal on a 2D screen, our softwares uses the method of raytracing. Basically, a virtual camera is simulated that shoots out rays across a defined field-of-view. The program tests the points on the ray until it either finds a point that is mathematically defined to be in the set or else travels out-of-bounds. If the ray hits the set, then the corresponding pixel on the virtual camera view plate is colored accordingly. To provide more definition to the image, fake shadows are added to the image by testing to see if a point in the set being renderered has a direct line to the virtual light source.
That's a very clipped overview of the subject. If you'd like to read up more, check out http://www.bugman123.com/Hypercomplex/index.html for all sorts of information and cool graphics of hypercomplex fractals.
"Autumn Sunset on the Mandelbulb": This view across the side of the fractal looks like trees in the fall, especially due to the coloring.
My team claims to have found the hidden "Mandelman" who lives in the Mandelbulb. Can you see his face?