Higher order Mandelbrot fractals
Higher order Mandelbrot fractals.
Mandelbrot applet.
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Description:
Mandelbrot sets are connected sets of points in the complex plane generated by transformations:
| Mandelbrot | Zn+1 = Z2n + C |
| Cubic Mandelbrot | Zn+1 = Z3n + C
|
| Quadratur Mandelbrot | Zn+1 = Z4n + C
|
| Penta Mandelbrot | Zn+1 = Z5n + C
|
| Hexa Mandelbrot | Zn+1 = Z6n + C
|
| Hepta Mandelbrot | Zn+1 = Z7n + C
|
where:
C = Re(C)+i*Im(C), Re(C) and Im(C) are x and y coordinates.
Initial value of Z = 0
For certain values of C, the result "levels off" after a while. For all others, it grows without limit.
If Zn remains within a distance of 2 of the origin forever, then the point C is said to be in the Mandelbrot set. If the sequence diverges from the origin, then the point is not in the set. There is a close relation between Julia sets and Mandelbrot set. For the points far inside the boundary the corresponding Julia set will be a circle. If the points are too far outside the boundary Julia sets break into scattered points.
Connection between Julia and Mandelbrot sets of higher order
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