American physicists investigated the statistical properties of the movements of Mexican jumping beans (the so-called boxes of Sebastiania pavoniana, which set the larvae of the leaflet growing in them in motion) in the absence of a temperature gradient. It turned out that in this case the motion is well described by the random walk model. The authors showed that such a strategy is more successful in finding the shadow than blind directional movement.
https://indico.ijs.si/event/1643/