Whitney Decomposition Duel

Auto‑shuffle mode: after every move the forbidden set is regenerated — no corner guarantees, denser and more irregular components, widely distributed.

Red path

Blue path

Forbidden area

Start/Goal bands

Rules.

Choose RED and BLUE starts on the thin green band at the middle-left.
From a current point P, your move must land somewhere on the circle centered at P whose radius equals the distance from P to the forbidden region.
The segment between your old and new points may not intersect the forbidden region.
First to touch the thick right goal band wins.
Auto‑shuffle: after each valid move, the forbidden set is replaced with a new dense, irregular arrangement (default On).

At the bottom: What is a “Whitney decomposition” (in brief)?

In analysis on domains with holes or rough boundaries, we often break the domain into a family of rectangles/squares whose sizes are comparable to their distances to the boundary; this is called a Whitney decomposition. It lets us control local behavior (e.g., estimates for functions or kernels) in a way that smoothly adapts to how close we are to the boundary. The spirit of this game mirrors that idea: step sizes are constrained by the distance to the forbidden set (a stand-in for a boundary), so moves naturally become smaller when you are near it and larger when you are far away.