Random walking and smart jumps
November 26th, 2010

An article in Physical Review Focus provokes some interesting thoughts about individual paths and encounters.

. . . . there is a class of random walks called Lévy flights, which include occasional long-distance jumps. The distribution of step sizes is described by a power law, which means that there are steps of all sizes and no well-defined “average” step size, at least for one class of Lévy flights. They have been observed in various natural settings, most famously in the search strategy of certain animals when food is scarce. For example, hungry sharks will typically scour back and forth over small areas, but if the search is fruitless, they will intermittently “jump” to new, far-off areas [1]. “People have also [studied] Lévy flights in stock prices, epidemics, and small world networks,” says Ajay Gopinathan, from the University of California, Merced. . . .
They believe further work in this direction could address optimization, such as what would be the best Lévy flight distribution for a predator stalking prey that moves with a distinct Lévy flight pattern. It might also be used in analyzing the distribution of long-range links for small world networks like Facebook.

It is not too big a jump to assume that mobs traveling digital networks use Levy flight patterns for smart moves.

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