The Mandelbulb procedural texture produces a texture pattern based on the Mandelbrot fractal formula (figure 1).
Figure 1: The Mandelbulb node and it's associated parameters
Iterations - The number of iterations to calculate, higher values will produce more detailed results.
Power - Multiplies the number of iterations, as values increase above 0 or decrease below 0, they will produce more fractal shapes
Ballout - Higher values will alter the detail along the edges of the fractal pattern.
Transform Input - Positions, scales, and rotates the surface texture.
Projection Input - Sets how the texture projects onto the surface.