Click in the bold cell to place dots. Use Move to drag a dot (any visible copy).
Auto rebuilds edges. Edit: click two dots to add/remove an edge.
Pick a shape, drag it to position, drag corners to reshape.
Show finds one matching. Random picks a different one each click.
Shuffles the current matching by random 4-cycle flips.
Save as image or JSON. Reset clears everything.
Scroll to zoom · Ctrl+drag to pan
A perfect matching is a way to pair every dot inside the region with exactly one partner, using only the edges that already exist. Every dot is used once.
There are usually many valid matchings. The simulation picks one and then slowly shuffles it to explore the others. Each small shuffle is called a flip.
What a flip does:
The result is still a valid matching, just a slightly different one. Repeating this many thousands of times produces a fresh random matching from the space of all valid ones.
Speed controls how many flips are attempted per animation frame. Higher values mix faster but update less smoothly.