Network flow
This is an example of a geometric flow on a graph. Vertices flow in the direction defined by the “sum” of all the edges connected to them, where the sum is defined by treating the edges as vectors. Vertices with a single edge do not move.
Left click to add points and right click to remove them.
Once you’ve added some points, right click and drag to add edges between the points. Left click and drag to move points.
Once you’ve added a few points and a few edges, click the toggle animation button to see it move.
Discrete curve shortening flow
Try clicking below to add points to form a closed polygon (you have to click at least twice before anything shows up), and then click the other buttons to make it do stuff. Once there are at least three points; the “normal vectors” at the vertices of the polygon are displayed. Then you can click the button below to move one timestep forward to simulate the motion of the polygon under the discrete curve shortening flow. When there are only two points remaining the flow degenerates, and when two points in the flow get two close we replace them with only one point; I guess in the mathematical case this doesn’t cause any problems but there are sure to be some small numerical ones (note the discontinuous motion of the normal vectors).
You can find a much better demonstration of (a slightly different form of) curve shortening flow here https://a.carapetis.com/csf/.
Note that this is still a work in progress so there are probably some bugs. If you find any I’d like to know. In particular there is one where some polygons disappear almost immediately; if you draw something that isn’t really small then it should be around for a few seconds at least, so just try again if it seems to mess up.