Higher order Julia fractals

Higher order Julia fractals

Julia applet.

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Description:
This type fractals was named for mathematician Gaston Julia (1893-1978). Fractals are generated by following algorithms:

Julia	Z_n+1 = Z²_n + C
Cubic Julia	Z_n+1 = Z³_n + C
Quadratur Julia	Z_n+1 = Z⁴_n + C
Penta Julia	Z_n+1 = Z⁵_n + C
Hexa Julia	Z_n+1 = Z⁶_n + C
Hepta Julia	Z_n+1 = Z⁷_n + C

in all cases:
C = Re(C)+i*Im(C), Re(C) and Im(C) are constants,
initial value of Z = (x-coordinate) + i*(y-coordinate)
This algorithm is similar to algoritm to generate Mandelbrot sets. There is a Julia set corresponding to every point on the complex plane (an infinite number of Julia sets). The most visually attractive Julia sets tend to be found for the C values equal to points of the Mandelbrot set just outside the boundary. If the points are 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.
Historically, the Julia sets came first. It was a while looking at the Mandelbrot set as an "index" of all the Julia sets' origins that Mandelbrot noticed its properites.
Connection between Julia and Mandelbrot set of higher orders

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