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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“He that has his chains knocked off, and the prison doors set open to him, is perfectly at liberty, because he may either go or stay, as he best likes; though his preference be determined to stay, by the darkness of the night, or illness of the weather, or want of other lodging. He ceases not to be free, though the desire of some convenience to be had there absolutely determines his preference, and makes him stay in his prison.”
—John Locke (1632–1704)
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