from Hacker News

Lakes of Wada

by ramgorur on 10/7/18, 4:40 AM with 15 comments

• by semi-extrinsic on 10/8/18, 10:13 PM

  So imagine you have three fluids that don't mix which are colored red, green, blue. You can make drops of these fluids on a piece of paper, and manipulate their shapes e.g. with a pipette.

  This article is saying that mathematically, it's possible to make three single, continuous but weirdly shaped drops of these fluids, that together fill a square, in a way such that if you consider the three drop outlines as seen from above (e.g. by a camera), they all have the same outline.

• by Roritharr on 10/8/18, 9:19 PM

  This entry needs a simple english page. I read the first paragraph and didn't understand anything.

• by fibo on 10/9/18, 8:27 AM

  It is one counterexample in Topology for the Jordan Curve Theorem.

• by vortico on 10/9/18, 1:05 AM

  Wada basins exist for any number of open sets. As you could probably guess from the article, the Newton method applied to x^n - 1 gives a Wada basin of n sets. These are fun counterexamples to the claim "given three nontrivial disjoint sets on a plane, their boundaries are not mutally equal."