Softology - Triplex Fractals Gallery

Triplex Fractals

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

SIN
Negative SIN
COS
Rucker
Reversed Order
Reversed Order Poistive Z
IQ
Negative IQ
Negative COS
Negative Rucker
Msltoe
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.

Mandelbulb formula z=z^p+c

More samples available in my Mandelbulb Gallery and Juliabulb Gallery.

Mandelbulb Power 8 SIN	Mandelbulb Power 8 Negative SIN	Mandelbulb Power 8 COS	Mandelbulb Power 8 Rucker
Mandelbulb Power 8 Reversed Order	Mandelbulb Power 8 Reversed Order Positive Z	Mandelbulb Power 8 IQ	Mandelbulb Power 8 Negative IQ
Mandelbulb Power 8 Negative COS	Mandelbulb Power 8 Negative Rucker	Mandelbulb Power 8 Msltoe	Mandelbulb Power 8 XpYp1
Mandelbulb Power 8 XpYp3	Mandelbulb Power 8 XpYn1	Mandelbulb Power 8 XnYp1	Mandelbulb Power 8 XnYn1
Mandelbulb Power 8 XpYn3	Mandelbulb Power 8 XnYp3	Mandelbulb Power 8 XnYn3	Mandelbulb Power 8 YpXp2
Mandelbulb Power 8 YpXp3	Mandelbulb Power 8 YpXn2	Mandelbulb Power 8 YnXp2	Mandelbulb Power 8 YnXn2
Mandelbulb Power 8 YpXn3	Mandelbulb Power 8 YnXp3	Mandelbulb Power 8 YnXn3	Mandelbulb Power 8 ZpXp2
Mandelbulb Power 8 ZpXp3	Mandelbulb Power 8 ZpXn2	Mandelbulb Power 8 ZnXp2	Mandelbulb Power 8 ZnXn2
Mandelbulb Power 8 ZpXn3	Mandelbulb Power 8 ZnXp3	Mandelbulb Power 8 ZnXn3	Mandelbulb Power 8 XpZp1
Mandelbulb Power 8 XpZp2	Mandelbulb Power 8 XpZn1	Mandelbulb Power 8 XnZp1	Mandelbulb Power 8 XnZn1
Mandelbulb Power 8 XpZn2	Mandelbulb Power 8 XnZp2	Mandelbulb Power 8 XnZn2	Mandelbulb Power 8 YpZp1
Mandelbulb Power 8 YpZp2	Mandelbulb Power 8 YpZn1	Mandelbulb Power 8 YnZp1	Mandelbulb Power 8 YnZn1
Mandelbulb Power 8 YpZn2	Mandelbulb Power 8 YnZp2	Mandelbulb Power 8 YnZn2	Mandelbulb Power 8 ZpYp3
Mandelbulb Power 8 ZnYp1	Mandelbulb Power 8 ZnYn1	Mandelbulb Power 8 ZnYp3	Mandelbulb Power 8 ZnYn3

Mandelbulb Power 2 SIN	Mandelbulb Power 2 Negative SIN	Mandelbulb Power 2 COS	Mandelbulb Power 2 Rucker
Mandelbulb Power 2 Reversed Order	Mandelbulb Power 2 Reversed Order Positive Z	Mandelbulb Power 2 IQ	Mandelbulb Power 2 Negative IQ
Mandelbulb Power 2 Negative COS	Mandelbulb Power 2 Negative Rucker	Mandelbulb Power 2 Msltoe

Phoenix formula z=z^p+c*lastz

More samples available in my Phoenix Mandelbulb Gallery and Phoenix Juliabulb Gallery.

Phoenix Power 8 SIN	Phoenix Power 8 Negative SIN	Phoenix Power 8 COS	Phoenix Power 8 Rucker
Phoenix Power 8 Reversed Order	Phoenix Power 8 Reversed Order Positive Z	Phoenix Power 8 IQ	Phoenix Power 8 Negative IQ
Phoenix Power 8 Negative COS	Phoenix Power 8 Negative Rucker	Phoenix Power 8 Msltoe	Phoenix Power 8 XpYp1
Phoenix Power 8 XpYp3	Phoenix Power 8 XpYn1	Phoenix Power 8 XnYp1	Phoenix Power 8 XnYn1
Phoenix Power 8 XpYn3	Phoenix Power 8 XnYp3	Phoenix Power 8 XnYn3	Phoenix Power 8 YpXp2
Phoenix Power 8 YpXp3	Phoenix Power 8 YpXn2	Phoenix Power 8 YnXp2	Phoenix Power 8 YnXn2
Phoenix Power 8 YpXn3	Phoenix Power 8 YnXp3	Phoenix Power 8 YnXn3	Phoenix Power 8 ZpXp2
Phoenix Power 8 ZpXp3	Phoenix Power 8 ZpXn2	Phoenix Power 8 ZnXp2	Phoenix Power 8 ZnXn2
Phoenix Power 8 ZpXn3	Phoenix Power 8 ZnXp3	Phoenix Power 8 ZnXn3	Phoenix Power 8 XpZp1
Phoenix Power 8 XpZp2	Phoenix Power 8 XpZn1	Phoenix Power 8 XnZp1	Phoenix Power 8 XnZn1
Phoenix Power 8 XpZn2	Phoenix Power 8 XnZp2	Phoenix Power 8 XnZn2	Phoenix Power 8 YpZp1
Phoenix Power 8 YpZp2	Phoenix Power 8 YpZn1	Phoenix Power 8 YnZp1	Phoenix Power 8 YnZn1
Phoenix Power 8 YpZn2	Phoenix Power 8 YnZp2	Phoenix Power 8 YnZn2	Phoenix Power 8 ZpYp3
Phoenix Power 8 ZnYp1	Phoenix Power 8 ZnYn1	Phoenix Power 8 ZnYp3	Phoenix Power 8 ZnYn3

Phoenix Power 3 SIN	Phoenix Power 3 Negative SIN	Phoenix Power 3 COS	Phoenix Power 3 Rucker
Phoenix Power 3 Reversed Order	Phoenix Power 3 Reversed Order Positive Z	Phoenix Power 3 IQ	Phoenix Power 3 Negative IQ
Phoenix Power 3 Negative COS	Phoenix Power 3 Negative Rucker	Phoenix Power 3 Msltoe

Polynomial1 formula z=z^p+z+c

More samples available in my Polynomial Mandelbulb Gallery and Polynomial Juliabulb Gallery.

Polynomial1 Power 8 SIN	Polynomial1 Power 8 Negative SIN	Polynomial1 Power 8 COS	Polynomial1 Power 8 Rucker
Polynomial1 Power 8 Reversed Order	Polynomial1 Power 8 Reversed Order Positive Z	Polynomial1 Power 8 IQ	Polynomial1 Power 8 Negative IQ
Polynomial1 Power 8 Negative COS	Polynomial1 Power 8 Negative Rucker	Polynomial1 Power 8 Negative Rucker

Polynomial1 Power 3 SIN	Polynomial1 Power 3 Negative SIN	Polynomial1 Power 3 COS	Polynomial1 Power 3 Rucker
Polynomial1 Power 3 Reversed Order	Polynomial1 Power 3 Reversed Order Positive Z	Polynomial1 Power 3 IQ	Polynomial1 Power 3 Negative IQ
Polynomial1 Power 3 Negative COS	Polynomial1 Power 3 Negative Rucker	Polynomial1 Power 3 Msltoe

Polynomial2 formula z=z^p-z+c

More samples available in my Polynomial Mandelbulb Gallery and Polynomial Juliabulb Gallery.

Polynomial2 Power 8 SIN	Polynomial2 Power 8 Negative SIN	Polynomial2 Power 8 COS	Polynomial2 Power 8 Rucker
Polynomial2 Power 8 Reversed Order	Polynomial2 Power 8 Reversed Order Positive Z	Polynomial2 Power 8 IQ	Polynomial2 Power 8 Negative IQ
Polynomial2 Power 8 Negative COS	Polynomial2 Power 8 Negative Rucker	Polynomial2 Power 8 Msltoe

Polynomial2 Power 2 SIN	Polynomial2 Power 2 Negative SIN	Polynomial2 Power 2 COS	Polynomial2 Power 2 Rucker
Polynomial2 Power 2 Reversed Order	Polynomial2 Power 2 Reversed Order Positive Z	Polynomial2 Power 2 IQ	Polynomial2 Power 2 Negative IQ
Polynomial2 Power 2 Negative COS	Polynomial2 Power 2 Negative Rucker	Polynomial2 Power 2 Msltoe

Manowar formula z=z^p+c+lastz

Manowar is a good example of how extending the triplex algebra to more complex (in this case only slightly more complex) formulas leads to dusty/disconnected results.

More samples available in my Manowar Mandelbulb Gallery and Manowar Juliabulb Gallery.

Manowar Power 8 SIN	Manowar Power 8 Negative SIN	Manowar Power 8 COS	Manowar Power 8 Rucker
Manowar Power 8 Reversed Order	Manowar Power 8 Reversed Order Positive Z	Manowar Power 8 IQ	Manowar Power 8 Negative IQ
Manowar Power 8 Negative COS	Manowar Power 8 Negative Rucker	Manowar Power 8 Msltoe

Manowar Power 4 SIN	Manowar Power 4 Negative SIN	Manowar Power 4 COS	Manowar Power 4 Rucker
Manowar Power 4 Reversed Order	Manowar Power 4 Reversed Order Positive Z	Manowar Power 4 IQ	Manowar Power 4 Negative IQ
Manowar Power 4 Negative COS	Manowar Power 4 Negative Rucker	Manowar Power 4 Msltoe

Ikenaga formula z=z^p+(c-1)*z-c

The Ikenaga formula also leads to more dusty and disconnected results but zoomed in images can give unique and interesting results.

More samples available in my Ikenaga Mandelbulb Gallery and Ikenaga Juliabulb Gallery.

Ikenaga Power 8 SIN	Ikenaga Power 8 Negative SIN	Ikenaga Power 8 COS	Ikenaga Power 8 Rucker
Ikenaga Power 8 Reversed Order	Ikenaga Power 8 Reversed Order Positive Z	Ikenaga Power 8 IQ	Ikenaga Power 8 Negative IQ
Ikenaga Power 8 Negative COS	Ikenaga Power 8 Negative Rucker	Ikenaga Power 8 Msltoe

Ikenaga Power 3 SIN	Ikenaga Power 3 Negative SIN	Ikenaga Power 3 COS	Ikenaga Power 3 Rucker
Ikenaga Power 3 Reversed Order	Ikenaga Power 3 Reversed Order Positive Z	Ikenaga Power 3 IQ	Ikenaga Power 3 Negative IQ
Ikenaga Power 3 Negative COS	Ikenaga Power 3 Negative Rucker	Ikenaga Power 3 Msltoe