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[GIF] Cops and Robbers (or Zombies and Humans): pursuit-evasion games

Posted 6 years ago
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Cops and Robbers is a mathematical game in which pursuers (cops) attempt to capture evaders (robbers). The game is one of many pursuit-evasion games, each of which is governed by a different set of rules. The general goal of these problems is to determine the number of pursuers required to capture a given number of evaders.

The GIFs above show two versions of the game. The first is similar to the standard Cops and Robbers rendition, and the second is best described as "Zombies and Humans".

In both versions, an evader moves in the direction that gets it furthest away from the pursuers (focusing more on the closer pursuers), and a pursuer moves in the direction that gets it closest to the evaders (focusing more on the closer evaders).

  • In the first simulation, members of both groups have a constant speed.
  • In the second simulation, members of a group move more quickly the closer they are to members of the opposite group, and slower when further away.

Additional sources not linked above:


Originally published at FOURIEST SERIES

Code:

3 Replies

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Very nice simulation. In many many pursuit, a key question is whether the pursuers are able to coordinate in any fashion. It is clearly not optimal for each pursuer to just aim towards the nearest pursuee. "Zombies" aren't going to coordinate, but "cops" can and do. Coordinated "cops" should steer toward areas other cops aren't able to cover. Then there is "leading" the pursued rather than aiming toward where they are now. It is a harder problem and there are multiple possible "strategies" for coordinated pursuit. I am just throwing this out there for those interested in taking this sort of model further.

Posted 6 years ago

Awesome simulation, Great job, congrats :)

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