Science and mathematics::Pattern


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Science and mathematics

Fractal model of a fern illustrating self-similarity

Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed.<ref>{{#invoke:Citation/CS1|citation |CitationClass=journal }}</ref> For example, any sequence of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>


Some mathematical rule-patterns can be visualised, and among these are those that explain patterns in nature including the mathematics of symmetry, waves, meanders, and fractals. 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 self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their formation can be simple (e.g. Lindenmayer systems describing tree shapes).<ref name="Mandelbrot1983">{{#invoke:citation/CS1|citation |CitationClass=book }}</ref>

In pattern theory, devised by Ulf Grenander, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner.<ref>{{#invoke:citation/CS1|citation |CitationClass=book }}</ref>

In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of patterns.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>

Pattern sections
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Science and mathematics