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.
Read more: Applied complex analysis