Surviving In Zombieland
When I hear the phrase "random walk", I remember learning about it in physics in high school, in particular, when trying to imagine how long it might take for a photon to escape from the sun. I never thought about it in relation to the likelihood of encountering zombies.
Physicist Davide Cassi at the UniversitÓ di Parma in Italy hasn't either, although the wording of his paper does seem somewhat suggestive. Here's the summary:
Target annihilation by diffusing particles in inhomogeneous geometries
The survival probability of immobile targets, annihilated by a population of random walkers on inhomogeneous discrete structures, such as disordered solids, glasses, fractals, polymer networks and gels, is analytically investigated. It is shown that, while it cannot in general be related to the number of distinct visited points, as in the case of homogeneous lattices, in the case of bounded coordination numbers its asymptotic behaviour at large times can still be expressed in terms of the spectral dimension, and its exact analytical expression is given. The results show that the asymptotic survival probability is site independent on recurrent structures, while on transient structures it can strongly depend on the target position, and such a dependence is explicitly calculated.
Cassi appears to suggest that you'd be safest from zombies while hiding in a large, complex environment (like a mall), as opposed to the wide open spaces. Since zombies are fictional, of course, you can only watch zombie movies and their characters to see if this approach works out.
(Zombieland movie poster)
So what do math models have to do with science fiction? Take a look at this interesting video about the development of game programs (in this case, Left 4 Dead).
While you're at it, you might want to brush up on the math of zombie attacks, just to be on the safe side.
From Target annihilation by diffusing particles in inhomogeneous geometries via Inside Science; thanks to Moira for the tip. Oh, and don't forget to google the phrase "random walk" to look for interesting articles.
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