"Cubist" Mandelbrot and Julia
What is it ? : These formulas split the Mandelbrot and the Julia set is little geometrical
areas.
The Parameters : The bigger the "resolution" is, the smaller the areas are. By specifying
an imaginary value for this parameter, you will rotate the "squares". If
you select "none" in the Function menu, the standard Mandelbrot (or Julia)
set is displayed.
Julia^2 and Mandelbrot^2
What is it ? : These formula are based on the following equation : Z = z^<power>
* z' + c where z' is iterated same time as z : Z' = z' * p1 + p2.
Powered C
What is it ? : This formula was discovered by chance. It displays a fractal pattern
in a circle.
The Parameters : Starting Point : As in a standard Julia, modifying this will change the fractal pattern. Power of z : This is the power to which z is raised at each iteration. The default value (1.5, 1) can seem strange, but it's only for such kind of value that the fractal is circular. Increasing the real part will strengthen the pattern (don't set values higher to 1). For the imaginary value, the smaller it is (in absolute value), the fainter the pattern becomes. Power of c : The power to which c is raised at each iteration. Setting an nonzero imaginary value will break the circle. As with the standard Julia, the real value gives the symetry of the pattern. If you want to have a more "global" view of the Powered C formula, you
may want to try Powered C Family.
Sierpinsky Plane
What is it ? : This formula is not very interesting in itself, but is great for the textures. VERY IMPORTANT : Just after you loaded the formula, if it doesn't seem working, change the "Center" in the location tab from (0,0) to something slightly different, like (0.000473849, 0.000028374675) or something like that. The "Scale Factor" parameter should be greater than one. The smaller
it is, the rougher the pattern will be.
Sierpinsky Triangle II
What is it ? : This formula draws the Sierpinski with a different algorithm from the
standard Fractint formula, so the result when combined with colorings is
different. It only draws isocel triangles (specify the bottom angles with
the Alpha parameter), but I added a parameter which allow you to stretch
it horizontally. You should be able to draw any triangle so. The offset
parameter allow you to translate the z the coloring is seeing. Try it with
Final Decomposition (in dmj.ucl)...
