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Mathematics is commonly described as the "Science of Pattern." Any sequence of numbers that may be modeled by a mathematical function is considered a pattern.
In Pattern theory, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner.
Patterns are common in many areas of mathematics. Recurring decimals are one example. These are repeating sequences of digits which repeat infinitely. For example, 1 divided by 81 will result in the answer 0.012345679... the numbers 0-9 (except 8) will repeat forever — 1/81 is a recurring decimal.
Fractals are mathematical patterns that are scale invariant. This means that the shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at. While the outer appearance of self-similar patterns can be quite complex, the rules needed to describe or produce their formation can be extremely simple (e.g. Lindenmayer systems for the description of tree shapes).
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