Mandelbulbs

The Mandelbulb is a three-dimensional fractal created as a volumetric version of the two-dimensional Mandelbrot set, generated by repeatedly transforming each point in space using spherical coordinate math and raising it to a chosen power, most famously power eight, before adding the original seed point back in. This iterative process produces endlessly detailed, self-similar forms with bulb-like lobes, ridges, and swirling patterns that occupy a dimensional space between a surface and a solid. Its complexity makes it useful in computer graphics, where ray-marching techniques render it for procedural landscapes, digital art, and visual effects. In scientific visualization, the Mandelbulb helps illustrate concepts in chaos theory and non-linear iterative systems, while architects and designers experiment with its geometry for generative structures. It is also widely used by researchers optimizing GPU rendering, volumetric shading, and distance-estimation algorithms because its structure provides a demanding benchmark for visual computation.