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Hailed as one of the most interesting elements of mathematics, chaos theory is a complex subject. It is a sub-discipline of mathematics that shows that outwardly what seems as arbitrary events can actually be a result of normal equations and obeys particular laws; and even small alterations can result in remarkably great consequences because of the complexity of the systems involved. It is also referred to as Non-linear dynamics.
Its understanding is required not only for mathematics but across all kinds of studies.
Small, apparent insignificant changes in the initial conditions can lead to drastic consequences and changes in the results.
The slightest error in measurement can completely change a prediction often rendering it useless. Since it’s difficult to know the minutest details especially at the initial stages of a complex system, it is impossible to get the absolute prediction.
It explores the transitions between order and disorder, which often occur in surprising ways.
Turmoil leads to two adjacent points in a complex system to end up in completely different positions after a certain amount of time has passed. Turbulence occurs at all scales so it becomes a complete mixture.
They are complex patterns which have the same statistical character as a whole. They come to being through simple repetitive processes. They follow mathematical structures where certain similar patterns keep occurring at progressively smaller scales (such as snowflakes).
They also describe arbitrary or chaotic phenomena like crystal growth and formation of galaxies. Nature is full of fractals like trees, clouds, seashells, tornadoes, etc.
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