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Fractal Types
XaoS supports many different fractal types. Here is some more information about them.
The Mandelbrot set is the most famous escape time fractal ever. It has the simple formula z=z2+c. See the Mandelbrot set tutorial chapter.
The Mandelbrot^3 fractal is a simple modification of the standard Mandelbrot set formula, using z=z3+c instead of z=z2+c.
Other derivations of the Mandelbrot set (Mandelbrot^4 and so on) use even higher powers. See the Higher-Power Mandelbrots tutorial chapter.
This is a less well-known fractal that Thomas Marsh discovered in Fractint and added to XaoS. It has an interesting shape when displayed in the alternative planes. See the Octo tutorial chapter.
The Newton Fractal uses Newton's approximation method for finding the roots of a polynomial. It uses the polynomial x3=1 and counts the number of iterations needed to reach the approximate value of the root. The Newton^4 variant uses the polynomial x4=1 instead. See the Newton's Method tutorial chapter.
This fractal doesn't have Julia sets, but XaoS is able to generate Julia-like sets which are also very interesting (they are sometimes called Nova Fractals).
These three formulas were described by British Mathematician Michael Barnsley in his book Fractals Everywhere. It produces very nice crystalline Julia sets. See the Barnsley's Formula tutorial chapter.
This fractal was discovered by Shigehiro Ushiki, and published in an article called "Phoenix" in IEEE Transactions on Circuits and Systems, Vol. 35, No. 7, July 1988, pp. 788-789. This formula produces very nice Julia sets. See the Phoenix tutorial chapter.
The Magnet formulas come from theoretical physics. They are so-named because the formulas are derived from the study of magnetic phase transitions. The formulas are detailed in The Beauty of Fractals pp 129. See the Magnet tutorial chapter.