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chaos

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Model behaviour

To study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of mathematical modelling.
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Swirling colours

Maths on the tube

During World Mathematical Year 2000 a sequence of posters were displayed month by month in the trains of the London Underground aiming to stimulate, fascinate - even infuriate passengers! Keith Moffatt tells us about three of the posters from the series.

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blurry image of people

Friends and strangers

Sometimes a mathematical object can be so big that, however disorderly we make the object, areas of order are bound to emerge. Imre Leader looks at the colourful world of Ramsey Theory.
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fractal

Fractal expressionism

In the late 1940s, American painter Jackson Pollock dripped paint from a can on to vast canvases rolled out across the floor of his barn. Richard P. Taylor explains that Pollock's patterns are really fractals - the fingerprint of Nature.

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Chaos in Numberland: The secret life of continued fractions

One of the most striking and powerful means of presenting numbers is completely ignored in the mathematics that is taught in schools, and it rarely makes an appearance in university courses. Yet the continued fraction is one of the most revealing representations of many numbers, sometimes containing extraordinary patterns and symmetries. John D. Barrow explains.
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Lyapunov exponent

Extracting beauty from chaos

Images based on Lyapunov Exponent fractals are very striking. Andy Burbanks explains what Lyapunov Exponents are, what the much misunderstood phenomenon of chaos really is, and how you can iterate functions to produce marvellous images of chaos from simple mathematics.