Julibrots

Nice Image Juliabrot type

(type=julibrot)

The Julibrot fractal type uses a general-purpose renderer for visualizing three dimensional solid fractals. Originally Mark Peterson developed this rendering mechanism to view a 3-D sections of a 4-D structure he called a "Julibrot". This structure, also called "layered Julia set" in the fractal literature, hinges on the relationship between the Mandelbrot and Julia sets. Each Julia set is created using a fixed value c in the iterated formula z^2 + c. The Julibrot is created by layering Julia sets in the x-y plane and continuously varying c, creating new Julia sets as z is incremented. The solid shape thus created is rendered by shading the surface using a brightness inversely proportional to the virtual viewer's eye.

Starting with Fractint version 18, the Julibrot engine can be used with other Julia formulas besides the classic z^2 + c. The first field on the Julibrot parameter screen lets you select which orbit formula to use.

You can also use the Julibrot renderer to visualize 3D cross sections of true four dimensional Quaternion and Hypercomplex fractals. The Julibrot Parameter Screens

Orbit Algorithm -
select the orbit algorithm to use. The available possibilities include 2-D Julia and both mandelbrot and Julia variants of the 4-D Quaternion and Hypercomplex fractals.

Orbit parameters -
the next screen lets you fill in any parameters belonging to the orbit algorithm. This list of parameters is not necessarily the same as the list normally presented for the orbit algorithm, because some of these parameters are used in the Julibrot layering process.

From/To Parameters -
These parameters allow you to specify the "Mandelbrot" values used to generate the layered Julias. The parameter c in the Julia formulas will be incremented in steps ranging from the "from" x and y values to the "to" x and y values. If the orbit formula is one of the "true" four dimensional fractal types quat, quatj, hypercomplex, or hypercomplexj, then these numbers are used with the 3rd and 4th dimensional values.

The "from/to" variables are different for the different kinds of orbit algorithm.

Distance between the eyes -
set this to 2.5 if you want a red/blue anaglyph image, 0 for a normal greyscale image.

Number of z pixels -
this sets how many layers are rendered in the screen z-axis. Use a higher value with higher resolution video modes.

The remainder of the parameters are needed to construct the red/blue picture so that the fractal appears with the desired depth and proper 'z' location. With the origin set to 8 inches beyond the screen plane and the depth of the fractal at 8 inches the default fractal will appear to start at 4 inches beyond the screen and extend to 12 inches if your eyeballs are 2.5 inches apart and located at a distance of 24 inches from the screen. The screen dimensions provide the reference frame.


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