#2019209 - safe, edit, edited screencap, screencap, twilight sparkle, alicorn, pony, g4, sparkle's seven, droste effect, eye reflection, faic, female, forever, fractal, narcissism, pudding face, recursion, reflection, smiling, solo, twilight sparkle (alicorn)

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6 comments posted

🂾𝕃𝕚𝕟𝕔𝕠𝕝𝕟𝔹𝕣𝕖𝕨𝕤𝕥𝕖𝕣𝔽𝕒𝕟🂽

Goodbye guys ;)

@Shimmering Spectacle

Reflectception

Nice :>

Posted 2 years ago Report

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furrypony

hopelessly sad filly

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.

Posted 4 years ago Report

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furrypony

hopelessly sad filly

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