Chaos theory is an interdisciplinary scientific theory and branch of mathematics focused on underlying patterns and deterministic laws, of dynamical systems, that are highly sensitive to initial conditions, that were once thought to have completely random states of disorder and irregularities.
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Chaos theory has applications in a variety of disciplines, including meteorology, anthropology, sociology, environmental science, computer science, engineering, economics, ecology, and pandemic crisis management.
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The theory formed the basis for such fields of study as complex dynamical systems, edge of chaos theory, and self-assembly processes.
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Chaos theory is a method of qualitative and quantitative analysis to investigate the behavior of dynamic systems that cannot be explained and predicted by single data relationships, but must be explained and predicted by whole, continuous data relationships.
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Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand.
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Chaos theory wanted to see a sequence of data again, and to save time he started the simulation in the middle of its course.
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Chaos theory did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation.
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Beforehand he had studied information Chaos theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy.
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Chaos theory was awarded the Wolf Prize in Physics in 1986 along with Mitchell J Feigenbaum for their inspiring achievements.
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Currently, chaos theory remains an active area of research, involving many different disciplines such as mathematics, topology, physics, social systems, population modeling, biology, meteorology, astrophysics, information theory, computational neuroscience, pandemic crisis management, etc.
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Some areas benefiting from chaos theory today are geology, mathematics, biology, computer science, economics, engineering, finance, meteorology, philosophy, anthropology, physics, politics, population dynamics, and robotics.
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Chaos theory can be found in ecological systems, such as hydrology.
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Chaos theory could be found in economics by the means of recurrence quantification analysis.
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In celestial mechanics, especially when observing asteroids, applying chaos theory leads to better predictions about when these objects will approach Earth and other planets.
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Chaos theory has been applied to environmental water cycle data, such as rainfall and streamflow.
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