Academic journal article Australian Mathematics Teacher

The Mandelbrot Set

Academic journal article Australian Mathematics Teacher

The Mandelbrot Set

Article excerpt

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On 1 March 1980 at the IBM Research Centre in New York State, the French mathematician Benoit Mandelbrot (1924-2010) looked at a black and white computer printout. On it he saw the complex shape that would later be called the Mandelbrot set. The discovery was featured in the August 1985 issue of Scientific American and the Mandelbrot set became a famous fractal with popular appeal.

It is one of the most extraordinary objects in mathematics. Zooming in to the intricate boundary reveals more and more detail and self-similarity with subtle variations. You could zoom in forever and continue to see new fractal worlds, even if you zoom in so far that the image is larger than the universe itself. It is often referred to as "the thumbprint of God".

In an article entitled Can We See the Mandelbrot Set?, John Ewing wrote:

   If the entire Mandelbrot set were placed on an ordinary sheet of
   paper, the tiny sections of boundary we examine would not fill the
   width of a hydrogen atom. Physicists think about such tiny objects;
   only mathematicians have microscopes fine enough to actually
   observe them.

Readily available software will allow you to create and explore the Mandelbrot set at home.

Creating a Mandelbrot set

A complex number can be shown on a number plane. …

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