a unique journey of fractal exploration

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A fractal, in the simplest of terms, is a graph.

Fractals are created from mathematical equations (functions).

By taking the output of the function, and using it as the starting point of the next calculation (many thousands of times), a fractal is created.

The Mandelbrot Set

The Mandelbrot Set

Fractals have been around since 1872 when Georg Cantor, a German mathematician, described Cantor Dust.

However, it wasn't until 1980 when Benoît Mandelbrot produced the first computer image of (what was later to be known as) the 'Mandelbrot Set' (see left) that the true beauty of fractals was realised. This is because the computer is the only really effective tool for producing images of such complexity.

Magnified section of the Mandelbrot SetThe Mandelbrot Set is the fractal that we will journey into on the web site. This fascinating image has been created with this simple mathematical function: z = z^2 + c (z starts at 0 and c varies).

Fractals are unique because they exhibit properties of self-similarity at many different scales. Thus, if you zoom into (magnify a portion of) a given fractal, you will see the same shapes and patterns appearing again and again. Theoretically, you can journey into the depths of a fractal in this way for ever.

By assigning simple rules for the colour values of a point when it is calculated by the mathematical function, the true beauty of a fractal emerges.     

[ Click here to take a voyage of discovery into the Mandelbrot Set ]

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