# Power laws occur when a random process triggers cascades or kills exponential processes Power laws follow the form of f(x) = ax^(-k) Imagine tree shaped graph  Now ‘trigger’ a node at random. A triggered node will trigger all its child nodes, and they will trigger their child nodes, etc. The size of these cascades follow [[Zipf’s Law]]. As the number of nodes in the system approaches infinity, the frequency of a cascade of a given size as a function of its size approaches a power law. You can also get a power law if you have a bunch of exponential growth processes that you kill off with a random distribution. Is this equivalent to the hierarchy + cascade? The cascades are exponential growth processes. And “killing” with equal probability at every time step ensures that the number of exponential processes you see is proportional to their size. I don’t think they’re the same mechanism except that they produce a distribution of exponential results whose frequency is proportional to their size, which is just by definition a power law. ### Related * [[neumannOneProcess2020]] * [[Sigmoid functions occur when a process has a rate proportional to the amount of a consumable or reversible and autocatalytic]]