Julia-like and Mandelbrot-like Phoenix Fractal comparison

 

 

Julia-like and Mandelbrot-like Phoenix Fractal comparison

 

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-like Phoenix sets press left mouse button (start point) and drag it to the end point. Line between points and corespoinding Julia-like Phoenix sets will be drawn by the applet.
Description:
Phoenix fractal is a connected set of points in the complex plane generated by transformation:
Z_n+1 = Z²_n + Re(C) + Im(C)*Z_n-1
where:
for Julia-like fractal:
C = Re(C)+i*Im(C), Re(C) and Im(C) are constants.
Initial value of Re(Z) and Im(Z) are x and y coordinates.
for Mandelbrot-like fractal:
C = Re(C)+i*Im(C), Re(C) and Im(C) are x and y coordinates.
Initial value of Z = 0
Phoenix curve was discovered by Shigehiro Ushiki IEEEE Transactions on Circuits and Systems vol 35 No. 7 July 1988 pp788.
Originally used values of C was: Re(C) = 0.56667, and Im(C) = -0.5.
There is no relation between Julia-like and Mandelbrot like Phoenix sets
Phoenix images do not have X and Y axis swappers as it is normal for this type.
Mandelbrot-like Phoenix set
Julia-like Phoenix set

 

 

 

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