Background: I have a function that outputs complex values.  I only care 
about input from the unit circle in the complex plane: (r,t) with r = |z| = 
1 and t = arg z in [0,1] (or [0,2*pi] if you prefer).  I could just make a 
3D plot with input the single real variable t and output x = Re f(t), y = 
Im f(t), except that the function I want to plot is f^n(t) - a 
self-composition, where I want to investigate what happens as n -> 
infinity.  So this would require re-writing my original function f(t) as a 
function f(x,y) even though it's actually a polar function f(r,t) with 
r=1.  Which I could do... but this work-around is now starting to feel 
really clunky.

Q1: Is there a better way?

Q2: Alternatively, is there an easy (less clunky that my alternative 
work-around) way to superimpose a (black or white) unit circle on top of my 
complex_plot of f^n?

Thanks!

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