The meaning of ergodic law refers to the law of universal experience. What we have to do is to ensure that each style appears once in each row or column. There is also a special case of ergodic law, as the name implies, which may examine gradual change. This rule needs to be compared between two graphs, and the change of the next graph depends on the shape of the previous graph.

The Origin and Theorem of Ergodicity

Ergodicity, also known as ergodicity theory, is a branch of mathematics that studies the asymptotic behavior of conservation transformation. It originates from the study of ergodic hypothesis which provides the basis for statistical mechanics, and is closely related to the mathematical branches such as dynamic system theory, probability theory, information theory, functional analysis and number theory.

Following Berkhow's average ergodicity theorem about point transformation, it is extended to the average ergodicity theorem of Markov process, and the individual ergodicity theorem on discrete semigroup φk is extended to more general one-parameter semigroup φt or even multi-parameter case, and so on.

Many mathematical researchers have obtained various ergodic theorems, including maximal ergodic theorem, uniform ergodic theorem, controlled ergodic theorem, local ergodic theorem, Abelian ergodic theorem and subadditive ergodic theorem. The spectral theory research of measurement-preserving transformation is an important topic related to ergodic theory and functional analysis.