@Shimmering Spectacle  

 
Nice :>

Let Twilight’s face be F (pretty much a closed disk). The Gaze Map is  
Gaze: P(F) → P(F),  
where P(F) is the set of all nonempty compact subsets of F.
 
For any subset S in P(F), Gaze(S) = two smaller copies of S scaled into each eye of Twilight.
 
Then it’s easy to show that Gaze has a unique fixed point in P(F), homeomorphic to the Cantor set
 
Proof: By not sure what theorem it is, P(F) is complete under Hausdorff metric. Gaze is a contraction mapping under Hausdorff metric. Then use contraction mapping theorem. For details, see
 
To show that the fixed point is actually homeomorphic to the Cantor set 2^ω, explicitly define the homeomorphism in the obvious way.

The fixed point of Twilight’s Gaze map is a set that’s homeomorphic to the Cantor set!  

@Beau Skunky  
you know what they all say… eyes are the window to the soul

You can see her soul!

Reflectception