This reminds me of something I was reading earlier (may be a HN thread) about how a possibly optimal procedure for searching an area when you have no information is called a "Lévy flight", which "is a random walk in which the step-lengths have a probability distribution that is heavy-tailed". It's distinct from Brownian motion which keeps you closer to the same area. If you wander too far around your mountain in small steps, you probably get away from the peak, but if you want to find another mountain peak, you have to take some much longer steps.