Julia - Mandelbrot Connection for higher order transformations

Julia - Mandelbrot Connection for higher order transformations

Instructions: To zoom in on an area, highlight it with mouse by pressing right button and dragging out a rectangle. To see changes in Julia sets press left mouse button (start point) and drag it to the end point. Line between points and corespoinding Julia sets will be drawn by the applet.
Description:
Applet draws Mandelbrot and Julia sets of the same order. Depending on computer speed it may take a while to see a picture.
Mandelbrot set is a connected set of points in the complex plane generated by transformations:

Square Mandelbrot	Z_n+1 = Z²_n + C
Cubic Mandelbrot	Z_n+1 = Z³_n + C
Quadratur Mandelbrot	Z_n+1 = Z⁴_n + C
Penta Mandelbrot	Z_n+1 = Z⁵_n + C
Hexa Mandelbrot	Z_n+1 = Z⁶_n + C
Hepta Mandelbrot	Z_n+1 = Z⁷_n + 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 Z_n 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.
Julia set is generated by following algorithms:

Square 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

where:
C = Re(C)+i*Im(C), Re(C) and Im(C) are constants,
initial value of Z = (x-coordinate) + i*(y-coordinate)

Some interesting changes in Julia sets are seen when the line crosses the boundary of Mandelbrot set. You can zoom in the Mandelbrot set to draw the line near boundary.

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