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John Cook is an applied mathematician working in Houston, Texas. His career has been a blend of research, software development, consulting, and management. John is a DZone MVB and is not an employee of DZone and has posted 164 posts at DZone. You can read more from them at their website. View Full User Profile

Fractal-Like Phase Plots

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Define f(z) = iz*exp(-z/sin(iz)) + 1 and g(z) = f(f(z)) + 2 for a complex argument z. Here’s what the phase plots of g look like.

The first image lets the real and imaginary parts of z range from -10 to 10.

This close-up plots real parts between -1 and 0, and imaginary part between -3 and -2.

The plots were produced with this Python code:

from mpmath import cplot, sin, exp

def f(z): return 1j*z*exp(-z/sin(1j*z)) + 1

def g(z): return f(f(z)) + 2

cplot(g, [-1,0], [-3,-2], points=100000)

The function g came from Visual Complex Functions.

Published at DZone with permission of John Cook, author and DZone MVB. (source)

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