2.36 Julibrots
(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.
2D Julia sets - complex number formula z' = f(z) + c
The "from/to" parameters change the values of c.
4D Julia sets - Quaternion or Hypercomplex formula z' = f(z) + c
The four dimensions of c are set by the orbit parameters.
The first two dimensions of z are determined by the corners values.
The third and fourth dimensions of z are the "to/from" variables.
4D Mandelbrot sets - Quaternion or Hypercomplex formula z' = f(z) + c
The first two dimensions of c are determined by the corners values.
The third and fourth dimensions of c are the "to/from" variables.
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.