IBM sandpile experiment, demonstrating self-organised criticality
Bak misunderstood uniformitarianism as meaning that change is always gradual. However, the deeper meaning of uniformitarianism is that extraordinary effects do not have to have extraordinary causes.In his famous sandpile experiment, Bak showed that a uniform input (sand falling onto a pile one grain at a time) could produce effects (avalanches of sand falling off the pile) on all scales. Small slippages occurred frequently, medium slippages less often, and large slippages very rarely (once the pile had 'self-organised' to the 'critical' state, that is). Contrary to Bak's view, this is a validation of the uniformitarian principle since it shows that large and unusual phenomena (big avalanches) can arise from the same processes as produce ordinary ones (the continual small avalanches).
Self-organised criticality shows how something like the extinction of the dinosaurs or the fall of the Roman empire need not require some special factor such as a meteorite impact or a barbarian invasion. It may come about through the same processes as lie behind smaller effects, such as the extinction of individual species or everyday fluctations in people's political and economic fortunes.
As used on this website, uniformitarianism means precisely this. History, despite its enormous variety, is to be understood not as a series of chance events with ad hoc causes, but as the expression of eternal and constant principles.