Phoenix Fractal
Phoenix Fractal
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Description:
Phoenix fractal is a connected set of points in the complex plane generated by transformation:
Zn+1 = Z2n + Re(C) + Im(C)*Zn-1
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.
Phoenix curve was discovered by Shigehiro Ushiki IEEEE Transactions on Circuits and Systems vol 35 No. 7 July 1988 pp788.
If Zn remains within a distance of 2 of the origin forever, then the point C is said to be in the Phoenix set. If the sequence diverges from the origin, then the point is not in the set, but 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.
Julia-like Phoenix set
Julia-like and Mandelbrot-like Phoenix sets comparison
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