Aliasing of the complex sinusoid. Or not.

I'm taking Discrete Time Signals and Systems, Part 1: Time Domain from Rice University on edX. One thing that gets mentioned is a phenomenom called aliasing where two complex sinusoids - of the form, y(n) = e j(ω n + φ) - are identical on the domain of integers if their frequencies differ by integer multiples of 2π.
Given the periodicity of sin and cos it's straightforward that this would be the case. But it's still kinda cool - I think - that such drastically different functions on the reals are the same when restricted to an integer domain.
Anyhow, I made this plotting tool to actually see the aliasing (or lack thereof) for pairs of complex sinusoids.

y1(n) = e j(ω n + φ) and y2(n) = e j((ω + 2 π m) n + φ) (Feel free to change the parameter values.)

ω:    φ:    m:   

Real Component Imaginary Component