Slope Formula Tutorial for UltraFractal - Page 3


Convergent Fractals

Some of the more interesting slope formulas derive from convergent fractals. Some convergent fractals have Mandelbrot-like and Julia-like regions. Others, such as the Newton fractal, don't have these regions. The most commonly used convergent method is the Newton method. Other convergence methods include Householder, Halley and Schroder. These alternate convergence methods are available for some of the convergent slope formulas in reb.ufm. 

The next 4 images illustrate the different convergence methods. The slope formula is Newton with power = (5,0), Magnification = 1.5, and defaults for the remaining parameters, except as noted. The coloring method is Direct Color Slope.

Convergence Method = Newton
Convergence Method = Householder
Convergence Method = Halley
Convergence Method = Schroder

The following two images were created with the formula default setting except as noted. The coloring method used was Direct Color Slope.

Cayley Mandel
Height Pre-Scale = 3
Cayley Julia
Height Pre-Scale = 0.04


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