|The following gallery shows examples of raytraced 3D fractals created using triplex algebra and variations of the triplex algebra. The orginal Mandelbulb fractal is the Mandelbulb Power 8 SIN image. Using combinations of formulas and variations leads to the images in this gallery.
Similar to variations of the 2D Mandelbrot formulas the more complex formulas do tend to create more complex and/or disconnected bulb fractals but the zoomed in fractals show unique details. The Mandelbulbs also allow Juliabulbs which are the same as the 2D Julia Sets with the c in z=z^p+c remaining constant during the calculations.
Many of the samples here may look very similar, but they all give unique results when rendered at larger sizes or when zooming in to the fractals. See the linked Flickr galleries to get an idea of the possible fractals that can be created.
All of these sample images were created with Visions of Chaos. NOTE: these images are purposely rendered in grayscale to best show the structures and shapes. To see them with various colors, lighting, zoom levels and shading, click the links to the Flickr gallery pages.
References For Variations
Reversed Order Poistive Z
Rotational Matrices - This document from Tad Boniecki covers the maths behind the remaining 48 XpYp1 etc variations.
Custom Trig 1 - Another 20 new variations of Mandelbulbs thanks to ideas from Tad.
Custom Trig 2 - Even more (27) new variations of Mandelbulbs thanks to ideas from Tad.