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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 was discovered by Thomas A. K. Kjaer in Fractint and he added it 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 p. 129. See the Magnet tutorial chapter.
This fractal was added to XaoS by Árpád Fekete.
This fractal was added to XaoS by Árpád Fekete.
The Mandelbar fractal (also known as Tricorn was introduced by Crowe, Hasson, Rippon and Strain-Clark in 1989.
The Lambda fractal is related to the logistic map, defined by Verhulst in 1845. Those parameters r belong to the fractal that produce a bounded iteration.
This fractal was taken from Fractint, contributed by Scott Taylor and Lee Skinner. It is defined by the formula zn+1=zn2+zn-1+c.
This fractal was taken from Fractint, contributed by Scott Taylor and Lee Skinner. It is defined by the Mandelbrot formula z=z2+c, but c is always overwritten with c=c/2+z for the next iteration.
This fractal is the well-known Sierpinski triangle.
This fractal is the well-known Sierpinski carpet.
This is the well-known (Koch Snowflake)https://en.wikipedia.org/wiki/Koch_snowflake), defined in 1904 by the Swedish mathematican Helge von Koch.
The Spidron figure was introduced by Dániel Erdély in 1979, but this shape is also known as a Baravelle spiral.
This fractal is a variant of the Sierpinski triangle. It is a contribution by Árpád Fekete.
This fractal type is contributed by Samuel Bizien and Árpád Fekete in 2007.
A simple self-similar fractal contributed by Árpád Fekete.
This is a variant of the Barsnley fractals.