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.
The mandelbrot set is calculated by the following formula:
The julia set is calculated by the following formula:
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.
The mandelbrot set is calculated by the following formula:
The julia set3 is calculated by the following formula:
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.
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.
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:
We do this by iterating the formula
This formula just takes the sine from a point in the complex plain.
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:
We do this by iterating the formula
Mandelbrot Set
Julia set
Mandelbrot Set3
Julia set3
Zn+1 = CZ( 1 - Zn )
Newton Raphson X3
Sin Z
Newton Raphson -X3 + 9 X 2 - 18X + C