Final Destination Topology

Panel 1: The mathematician: I see you are playing Super Smash Bros Melee. I like that game. Man: Yeah, my favorite level is Final Destination. It's the most balanced level. Panel 2: The mathematician: What is wrong with you people? Final Destination is just a flat line. Panel 3: It's not the most balanced level, it's heavily biased towards certain characters because the number of valid manuevers is severly restricted. I can draw final destination with my left hand. -------------------- The stage is completely flat. It's a line. That's the most boring topological shape ever. It's not only simply connected, it's also convex. Panel 4: The mathematician: They should make a level that is non-Hausdorff. Man: How do you represent a non-metric space in a video game? The mathematician: It would be awesome.

Personally, I'd even advocate turning items on given that the probability distribution of their spawn points is known to all players. I also think time is a better format than stock for more than two players.

Final Destination Topology

3 August 2007