A segment breaks at a uniformly random point, each piece breaks again, recursively. After N generations, 2^N fragments remain. The distribution of log-fragment sizes is Gaussian (log-normal distribution), with power-law tails emerging from correlated cascades.
Log-normal: log(fragment size) ~ Gaussian, by the multiplicative central limit theorem. Each break multiplies by a random fraction — products of random numbers → log-normal. Power-law fragments emerge in correlated (preferential) fragmentation.