I don't think jus the raw distance (from here) is the metric to necessarily optimize for. It may be more useful to throughly search the nearby area, for example - especially if you feel you're in a good neighborhood already.

https://www.sciencenews.org/article/sharks-use-math-hunt

A new study suggests that some sharks and other marine predators can follow strict mathematical strategies when foraging for dinner. The work, reported online June 9 in Nature, is the latest aiming to show whether animals sometimes move in a pattern called a Lévy walk.

Unlike random motion — in which animals take similar-sized steps in any direction, like a drunk stumbling around — Lévy walks are punctuated by rare, long forays in any direction. Draw a Lévy walk on a graph, and its squiggly pattern echoes a fractal, the mathematical phenomenon whose shape remains similar no matter the viewing scale.