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# Markov Chain
Markov chain is a relatively simple [stochastic](stochastic.md) (working with [probability](probability.md)) [mathematical](math.md) [model](model.md) for predicting or generating sequences of symbols. It can be used to describe some processes happening in the [real world](irl.md) such as behavior of some animals, Brownian motion or structure of a [language](human_language.md). In the world of [programming](programming.md) Markov chains are pretty often used for generation of texts that look like some template text whose structure is learned by the Markov chain (Markov chains are one possible model used in [machine learning](machine_learning.md)). Chatbots are just one example.
Markov chain is a relatively simple [stochastic](stochastic.md) (working with [probability](probability.md)) [mathematical](math.md) [model](model.md) that captures a "statistical structure" of a sequence of symbols (words, letters, [numbers](number.md), [musical](music.md) notes, ...) and is typically used for predicting or generating such sequences. It can very well describe certain processes that occur in the [real world](irl.md) such as behavior of some animals, Brownian motion or structure of [human language](human_language.md). In [programming](programming.md) Markov chains are pretty often used for generating "random" text that resembles given sample text -- Markov chain learns the structure of the sample text by computing probabilities of words following other words and then generates a new text so that these probabilities are preserved (of course, the new text will be a nonsensical gibberish from linguistic point of view, but it will resemble the template text statistically and "visually"). Chatbots and [procedural generation](procgen.md) are just some examples of where we might encounter Markov chains. This is however not where the use cases end -- an advanced use of Markov chain may be for example identification of the text author by the writing style, since it can be assumed that different authors prefer to use different words, phrases and idioms which will show in the generated Markov chain, and comparing these to the chain generated from the anonymous writing may give away the true author.
There are different types of Markov chains. Here we will be focusing on discrete time Markov chains with finite state space as these are the ones practically always used in programming. They are also the simplest ones.