There is a fundamental difference between explaining how a given entity behaves and generating it mathematically.

An observer studying the behaviour of an apple, for example the distance it falls in a given time, may come up with a mathematical formula that describes the behaviour of the apple.

This presupposes the existence of trees, apples and gravitational acceleration amongst other things.

Contrast this to an equation that defines a fractal function, for example iterating *z*^{2}+c to make the Mandelbrot set. In this case the formula does not describe the behaviour, but actually generates the set.

The search for a “Grand Unified Theory” in physics has centred on finding a set of equations that describe all known physical phenomena. Even if you found a set of formulae that precisely relate all particle properties, you would be no step further along the way to explaining why they behave this way.

Here we are looking for a formula that generates the world, not a set of formulae that describes its behaviour.

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