Markov Chains
If the function can be described by a stochastic matrix, that is, a matrix whose rows or columns sum to one, then the iterated system is known as a Markov chain.
Read more about this topic: Iterated Function
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“Of all men living [priests] are our greatest enemies. If it were possible, they would extinguish the very light of nature, turn the world into a dungeon, and keep mankind for ever in chains and darkness.”
—George Berkeley (1685–1753)