Fractal Algorithm's

There is, probably, an unlimited amount of fractal algorithm's. A few of them are incorparated in FracHunt. It is not possible to add your own formula's to FracHunt. However if you have this great formula I am eager to include it in a future version of FracHunt.

The following chapters will explain the algorithm's contained in FracHunt.

All the algorithm's in FracHunt iterate a formula until a maximum number of iterations is exceeded or the resulting vector exceeds a minimum or maximum value in which case a certain fixed color is used . When a minimum or maximum value is exceeded a certain color is selected depending on the number ot iterations and the coloring algorithm.

In the following chapters Z depicts a complex number.

Mandelbrot Set

The mandelbrot set is calculated by the following formula:

Zn+1 = Zn2 + Z

Julia set

The julia set is calculated by the following formula:

Zn+1 = Zn2 + C

If you compare this formula with the mandelbrot formula you will note that for the point where C equals Z the julia set is the same as the mandelbrot set. Therefore you could imagine a point in the mandelbrot set as an index into a julia set.

Mandelbrot Set3

The mandelbrot set is calculated by the following formula:

Zn+1 = Zn3 + Z

Julia set3

The julia set3 is calculated by the following formula:

Zn+1 = Zn3 + C

Of course for the point where C equals Z the julia set is the same as the mandelbrot set3. Therefore you could see a point in the mandelbrot set3 as an index into a julia set3.

Zn+1 = CZ( 1 - Zn )

Just a formula I saw on the web somewhere. It is not the greatest but it gives you something different to render than mandelbrot and julia sets.

Zn+1 = CZ( 1 - Zn )

Newton Raphson X3

Newton Raphson is a method used in numerical analysis to find the root of a formula. So we are trying to find the complex value for which a formula evaluates to zero. In FracHunt we actually try to find the point for which the following condition is met:

Z3 - C = 0

We do this by iterating the formula

Zn+1 = Zn - ( Z - C )3 / ( 3 ( Z - C )2 )

Sin Z

This formula just takes the sine from a point in the complex plain.

Zn+1 = C sin( Zn )

Newton Raphson -X3 + 9 X 2 - 18X + C

Newton Raphson is a method used in numerical analysis to find the root of a formula. So we are trying to find the complex value for which a formula evaluates to zero. In FracHunt we actually try to find the point for which the following condition is met:

Z3 - C = 0

We do this by iterating the formula

Zn+1 = Zn - ( -X3 + 9X2 - 18X + C ) / ( -3 X2 + 18X - 18 )
Copyright 2000,2004 by Ron AF Greve "http://informationsuperhighway.eu+31878753207