Iteration involves feeding the results of an equation back into the equation to generate a new result.

of x2 + 1/4, x2 - 3/4 and other formulae

Iteration can be used to find a cube root. Finding Cube Roots

This example generates lots of numbers and leads to the kind of question that mathematicians like to ponder - is it possible to prove that the number pattern generated always produces 1? Iteration Example.

Iteration has been used extensively in the generation of fractals and the research of chaos. Some dynamic systems, such as weather, climate and ocean currents are so complex that they cannot be described by mathematical equations. Meteorologists have suggested that an event as small as the beating of a single butterfly's wings can generate, through its impact on other factors in the environment, a major storm on the other side of the world. This can be modelled in a spreadsheet. Lorenz and the butterfly effect.

The mathematician Bénoit Mandelbrot used a deceptively simple iterated equation to generate his famous 'Mandelbrot set' (which re-introduced psychedelia to a new generation and a million t-shirt designs.

The biologist Robert May used iteration to model the behaviour of populations and found that there was chaotic behaviour when the inputs were set to certain values. Population.

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