The BTW sandpile model: add grains one at a time; when a site reaches threshold z_c=4, it topples, sending 1 grain to each neighbor. Avalanche sizes follow a power law P(s)~s^{-1.2}.
SOC (Bak, Tang, Wiesenfeld 1987): the system self-tunes to criticality without parameter tuning. Critical exponent τ≈1.2 for BTW in 2D. Large avalanches are rare but inevitable.