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

Mandelbulb formula z=z^p+c Power 2
More samples available in my Mandelbulb Gallery and Juliabulb Gallery.
Mandelbulb Power 2 SIN
Mandelbulb Power 2 SIN
Mandelbulb Power 2 Negative SIN
Mandelbulb Power 2 Negative SIN
Mandelbulb Power 2 COS
Mandelbulb Power 2 COS
Mandelbulb Power 2 Rucker
Mandelbulb Power 2 Rucker
Mandelbulb Power 2 Reversed Order
Mandelbulb Power 2 Reversed Order
Mandelbulb Power 2 Reversed Order Positive Z
Mandelbulb Power 2 Reversed Order Positive Z
Mandelbulb Power 2 IQ
Mandelbulb Power 2 IQ
Mandelbulb Power 2 Negative IQ
Mandelbulb Power 2 Negative IQ
Mandelbulb Power 2 Negative COS
Mandelbulb Power 2 Negative COS
Mandelbulb Power 2 Negative Rucker
Mandelbulb Power 2 Negative Rucker
Mandelbulb Power 2 Msltoe
Mandelbulb Power 2 Msltoe

Phoenix formula z=z^p+c*lastz Power 8
More samples available in my Phoenix Mandelbulb Gallery and Phoenix Juliabulb Gallery.
Phoenix Power 8 SIN
Phoenix Power 8 SIN
Phoenix Power 8 Negative SIN
Phoenix Power 8 Negative SIN
Phoenix Power 8 COS
Phoenix Power 8 COS
Phoenix Power 8 Rucker
Phoenix Power 8 Rucker
Phoenix Power 8 Reversed Order
Phoenix Power 8 Reversed Order
Phoenix Power 8 Reversed Order Positive Z
Phoenix Power 8 Reversed Order Positive Z
Phoenix Power 8 IQ
Phoenix Power 8 IQ
Phoenix Power 8 Negative IQ
Phoenix Power 8 Negative IQ
Phoenix Power 8 Negative COS
Phoenix Power 8 Negative COS
Phoenix Power 8 Negative Rucker
Phoenix Power 8 Negative Rucker
Phoenix Power 8 Msltoe
Phoenix Power 8 Msltoe
Phoenix Power 8 XpYp1
Phoenix Power 8 XpYp1
Phoenix Power 8 XpYp3
Phoenix Power 8 XpYp3
Phoenix Power 8 XpYn1
Phoenix Power 8 XpYn1
Phoenix Power 8 XnYp1
Phoenix Power 8 XnYp1
Phoenix Power 8 XnYn1
Phoenix Power 8 XnYn1
Phoenix Power 8 XpYn3
Phoenix Power 8 XpYn3
Phoenix Power 8 XnYp3
Phoenix Power 8 XnYp3
Phoenix Power 8 XnYn3
Phoenix Power 8 XnYn3
Phoenix Power 8 YpXp2
Phoenix Power 8 YpXp2
Phoenix Power 8 YpXp3
Phoenix Power 8 YpXp3
Phoenix Power 8 YpXn2
Phoenix Power 8 YpXn2
Phoenix Power 8 YnXp2
Phoenix Power 8 YnXp2
Phoenix Power 8 YnXn2
Phoenix Power 8 YnXn2
Phoenix Power 8 YpXn3
Phoenix Power 8 YpXn3
Phoenix Power 8 YnXp3
Phoenix Power 8 YnXp3
Phoenix Power 8 YnXn3
Phoenix Power 8 YnXn3
Phoenix Power 8 ZpXp2
Phoenix Power 8 ZpXp2
Phoenix Power 8 ZpXp3
Phoenix Power 8 ZpXp3
Phoenix Power 8 ZpXn2
Phoenix Power 8 ZpXn2
Phoenix Power 8 ZnXp2
Phoenix Power 8 ZnXp2
Phoenix Power 8 ZnXn2
Phoenix Power 8 ZnXn2
Phoenix Power 8 ZpXn3
Phoenix Power 8 ZpXn3
Phoenix Power 8 ZnXp3
Phoenix Power 8 ZnXp3
Phoenix Power 8 ZnXn3
Phoenix Power 8 ZnXn3
Phoenix Power 8 XpZp1
Phoenix Power 8 XpZp1
Phoenix Power 8 XpZp2
Phoenix Power 8 XpZp2
Phoenix Power 8 XpZn1
Phoenix Power 8 XpZn1
Phoenix Power 8 XnZp1
Phoenix Power 8 XnZp1
Phoenix Power 8 XnZn1
Phoenix Power 8 XnZn1
Phoenix Power 8 XpZn2
Phoenix Power 8 XpZn2
Phoenix Power 8 XnZp2
Phoenix Power 8 XnZp2
Phoenix Power 8 XnZn2
Phoenix Power 8 XnZn2
Phoenix Power 8 YpZp1
Phoenix Power 8 XpZp1
Phoenix Power 8 YpZp2
Phoenix Power 8 YpZp2
Phoenix Power 8 YpZn1
Phoenix Power 8 YpZn1
Phoenix Power 8 YnZp1
Phoenix Power 8 YnZp1
Phoenix Power 8 YnZn1
Phoenix Power 8 YnZn1
Phoenix Power 8 YpZn2
Phoenix Power 8 YpZn2
Phoenix Power 8 YnZp2
Phoenix Power 8 YnZp2
Phoenix Power 8 YnZn2
Phoenix Power 8 YnZn2
Phoenix Power 8 ZpYp3
Phoenix Power 8 ZpYp3
Phoenix Power 8 ZnYp1
Phoenix Power 8 ZnYp1
Phoenix Power 8 ZnYn1
Phoenix Power 8 ZnYn1
Phoenix Power 8 ZnYp3
Phoenix Power 8 ZnYp3
Phoenix Power 8 ZnYn3
Phoenix Power 8 ZnYn3

Phoenix formula z=z^p+c*lastz Power 3
More samples available in my Phoenix Mandelbulb Gallery and Phoenix Juliabulb Gallery.
Phoenix Power 3 SIN
Phoenix Power 3 SIN
Phoenix Power 3 Negative SIN
Phoenix Power 3 Negative SIN
Phoenix Power 3 COS
Phoenix Power 3 COS
Phoenix Power 3 Rucker
Phoenix Power 3 Rucker
Phoenix Power 3 Reversed Order
Phoenix Power 3 Reversed Order
Phoenix Power 3 Reversed Order Positive Z
Phoenix Power 3 Reversed Order Positive Z
Phoenix Power 3 IQ
Phoenix Power 3 IQ
Phoenix Power 3 Negative IQ
Phoenix Power 3 Negative IQ
Phoenix Power 3 Negative COS
Phoenix Power 3 Negative COS
Phoenix Power 3 Negative Rucker
Phoenix Power 3 Negative Rucker
Phoenix Power 3 Msltoe
Phoenix Power 3 Msltoe

Polynomial 1 formula z=z^p+z+c Power 8
More samples available in my Polynomial 1 Mandelbulb Gallery and Polynomial 1 Juliabulb Gallery.
Polynomial 1 Power 8 SIN
Polynomial 1 Power 8 SIN
Polynomial 1 Power 8 Negative SIN
Polynomial 1 Power 8 Negative SIN
Polynomial 1 Power 8 COS
Polynomial 1 Power 8 COS
Polynomial 1 Power 8 Rucker
Polynomial 1 Power 8 Rucker
Polynomial 1 Power 8 Reversed Order
Polynomial 1 Power 8 Reversed Order
Polynomial 1 Power 8 Reversed Order Positive Z
Polynomial 1 Power 8 Reversed Order Positive Z
Polynomial 1 Power 8 IQ
Polynomial 1 Power 8 IQ
Polynomial 1 Power 8 Negative IQ
Polynomial 1 Power 8 Negative IQ
Polynomial 1 Power 8 Negative COS
Polynomial 1 Power 8 Negative COS
Polynomial 1 Power 8 Negative Rucker
Polynomial 1 Power 8 Negative Rucker
Polynomial 1 Power 8 Msltoe
Polynomial 1 Power 8 Msltoe

Polynomial 1 formula z=z^p+z+c Power 3
More samples available in my Polynomial 1 Mandelbulb Gallery and Polynomial 1 Juliabulb Gallery.
Polynomial 1 Power 3 SIN
Polynomial 1 Power 3 SIN
Polynomial 1 Power 3 Negative SIN
Polynomial 1 Power 3 Negative SIN
Polynomial 1 Power 3 COS
Polynomial 1 Power 3 COS
Polynomial 1 Power 3 Rucker
Polynomial 1 Power 3 Rucker
Polynomial 1 Power 3 Reversed Order
Polynomial 1 Power 3 Reversed Order
Polynomial 1 Power 3 Reversed Order Positive Z
Polynomial 1 Power 3 Reversed Order Positive Z
Polynomial 1 Power 3 IQ
Polynomial 1 Power 3 IQ
Polynomial 1 Power 3 Negative IQ
Polynomial 1 Power 3 Negative IQ
Polynomial 1 Power 3 Negative COS
Polynomial 1 Power 3 Negative COS
Polynomial 1 Power 3 Negative Rucker
Polynomial 1 Power 3 Negative Rucker
Polynomial 1 Power 3 Msltoe
Polynomial 1 Power 3 Msltoe

Polynomial 2 formula z=z^p-z+c Power 8
More samples available in my Polynomial 2 Mandelbulb Gallery and Polynomial 2 Juliabulb Gallery.
Polynomial 2 Power 8 SIN
Polynomial 2 Power 8 SIN
Polynomial 2 Power 8 Negative SIN
Polynomial 2 Power 8 Negative SIN
Polynomial 2 Power 8 COS
Polynomial 2 Power 8 COS
Polynomial 2 Power 8 Rucker
Polynomial 2 Power 8 Rucker
Polynomial 2 Power 8 Reversed Order
Polynomial 2 Power 8 Reversed Order
Polynomial 2 Power 8 Reversed Order Positive Z
Polynomial 2 Power 8 Reversed Order Positive Z
Polynomial 2 Power 8 IQ
Polynomial 2 Power 8 IQ
Polynomial 2 Power 8 Negative IQ
Polynomial 2 Power 8 Negative IQ
Polynomial 2 Power 8 Negative COS
Polynomial 2 Power 8 Negative COS
Polynomial 2 Power 8 Negative Rucker
Polynomial 2 Power 8 Negative Rucker
Polynomial 2 Power 8 Msltoe
Polynomial 2 Power 8 Msltoe

Polynomial 2 formula z=z^p-z+c Power 2
More samples available in my Polynomial 2 Mandelbulb Gallery and Polynomial 2 Juliabulb Gallery.
Polynomial 2 Power 2 SIN
Polynomial 2 Power 2 SIN
Polynomial 2 Power 2 Negative SIN
Polynomial 2 Power 2 Negative SIN
Polynomial 2 Power 2 COS
Polynomial 2 Power 2 COS
Polynomial 2 Power 2 Rucker
Polynomial 2 Power 2 Rucker
Polynomial 2 Power 2 Reversed Order
Polynomial 2 Power 2 Reversed Order
Polynomial 2 Power 2 Reversed Order Positive Z
Polynomial 2 Power 2 Reversed Order Positive Z
Polynomial 2 Power 2 IQ
Polynomial 2 Power 2 IQ
Polynomial 2 Power 2 Negative IQ
Polynomial 2 Power 2 Negative IQ
Polynomial 2 Power 2 Negative COS
Polynomial 2 Power 2 Negative COS
Polynomial 2 Power 2 Negative Rucker
Polynomial 2 Power 2 Negative Rucker
Polynomial 2 Power 2 Msltoe
Polynomial 2 Power 2 Msltoe

Manowar formula z=z^p+c+lastz Power 8
More samples available in my Manowar Mandelbulb Gallery and Manowar Juliabulb Gallery.
Manowar Power 8 SIN
Manowar Power 8 SIN
Manowar Power 8 Negative SIN
Manowar Power 8 Negative SIN
Manowar Power 8 COS
Manowar Power 8 COS
Manowar Power 8 Rucker
Manowar Power 8 Rucker
Manowar Power 8 Reversed Order
Manowar Power 8 Reversed Order
Manowar Power 8 Reversed Order Positive Z
Manowar Power 8 Reversed Order Positive Z
Manowar Power 8 IQ
Manowar Power 8 IQ
Manowar Power 8 Negative IQ
Manowar Power 8 Negative IQ
Manowar Power 8 Negative COS
Manowar Power 8 Negative COS
Manowar Power 8 Negative Rucker
Manowar Power 8 Negative Rucker
Manowar Power 8 Msltoe
Manowar Power 8 Msltoe

Manowar formula z=z^p+c+lastz Power 4
More samples available in my Manowar Mandelbulb Gallery and Manowar Juliabulb Gallery.
Manowar Power 4 SIN
Manowar Power 4 SIN
Manowar Power 4 Negative SIN
Manowar Power 4 Negative SIN
Manowar Power 4 COS
Manowar Power 4 COS
Manowar Power 4 Rucker
Manowar Power 4 Rucker
Manowar Power 4 Reversed Order
Manowar Power 4 Reversed Order
Manowar Power 4 Reversed Order Positive Z
Manowar Power 4 Reversed Order Positive Z
Manowar Power 4 IQ
Manowar Power 4 IQ
Manowar Power 4 Negative IQ
Manowar Power 4 Negative IQ
Manowar Power 4 Negative COS
Manowar Power 4 Negative COS
Manowar Power 4 Negative Rucker
Manowar Power 4 Negative Rucker
Manowar Power 4 Msltoe
Manowar Power 4 Msltoe

Ikenaga formula z=z^p+z+c Power 8
More samples available in my Ikenaga Mandelbulb Gallery and Ikenaga Juliabulb Gallery.
Ikenaga Power 8 SIN
Ikenaga Power 8 SIN
Ikenaga Power 8 Negative SIN
Ikenaga Power 8 Negative SIN
Ikenaga Power 8 COS
Ikenaga Power 8 COS
Ikenaga Power 8 Rucker
Ikenaga Power 8 Rucker
Ikenaga Power 8 Reversed Order
Ikenaga Power 8 Reversed Order
Ikenaga Power 8 Reversed Order Positive Z
Ikenaga Power 8 Reversed Order Positive Z
Ikenaga Power 8 IQ
Ikenaga Power 8 IQ
Ikenaga Power 8 Negative IQ
Ikenaga Power 8 Negative IQ
Ikenaga Power 8 Negative COS
Ikenaga Power 8 Negative COS
Ikenaga Power 8 Negative Rucker
Ikenaga Power 8 Negative Rucker
Ikenaga Power 8 Msltoe
Ikenaga Power 8 Msltoe

Ikenaga formula z=z^p+z+c Power 3
More samples available in my Ikenaga Mandelbulb Gallery and Ikenaga Juliabulb Gallery.
Ikenaga Power 3 SIN
Ikenaga Power 3 SIN
Ikenaga Power 3 Negative SIN
Ikenaga Power 3 Negative SIN
Ikenaga Power 3 COS
Ikenaga Power 3 COS
Ikenaga Power 3 Rucker
Ikenaga Power 3 Rucker
Ikenaga Power 3 Reversed Order
Ikenaga Power 3 Reversed Order
Ikenaga Power 3 Reversed Order Positive Z
Ikenaga Power 3 Reversed Order Positive Z
Ikenaga Power 3 IQ
Ikenaga Power 3 IQ
Ikenaga Power 3 Negative IQ
Ikenaga Power 3 Negative IQ
Ikenaga Power 3 Negative COS
Ikenaga Power 3 Negative COS
Ikenaga Power 3 Negative Rucker
Ikenaga Power 3 Negative Rucker
Ikenaga Power 3 Msltoe
Ikenaga Power 3 Msltoe