Fractals





Fractals are objects that have fractional dimension.

Wow, isn't that a lot of help!!

Here is how this idea came up. If you try to measure a non-exotic object like a randomly-flopped garden hose with a ruler, the number you get for the length will depend on the length of the ruler.

A six foot ruler will give only a crude approximation to the length of the hose. A six inch ruler "flip-walked" along the hose does a better job.

As you use smaller and smaller rulers you converge on (get closer and closer to) the actual length of the hose.

With a fractal object, like a coastline, the smaller you make your ruler, the longer the coastline gets. This is because smaller and smaller rulers measure smaller and smaller jigs and jags in the coastline and fractals objects have jigs and jags on all scales. They do not start to look smooth as you magnify them.


In other words, a fractal is a mathematical object that is self-similar and chaotic. Fractals are infinitely complex: the closer you look the more detail you see. Most fractals are generated by a relatively simple equation where the results are fed back into the equation until it grows larger than a certain boundary. Most fractals are just a graph of an equation using complex numbers. The real line is the X-axis. The imaginary number line is the Y-axis. The point is fed into the equation such as the one for the Mandelbrot set.


Exhibits || Lexicon || Timeline

The Exploratorium, 1996

Fractals

Fractals





Fractals are objects that have fractional dimension.

Wow, isn't that a lot of help!!

Here is how this idea came up. If you try to measure a non-exotic object like a randomly-flopped garden hose with a ruler, the number you get for the length will depend on the length of the ruler.

A six foot ruler will give only a crude approximation to the length of the hose. A six inch ruler "flip-walked" along the hose does a better job.

As you use smaller and smaller rulers you converge on (get closer and closer to) the actual length of the hose.

With a fractal object, like a coastline, the smaller you make your ruler, the longer the coastline gets. This is because smaller and smaller rulers measure smaller and smaller jigs and jags in the coastline and fractals objects have jigs and jags on all scales. They do not start to look smooth as you magnify them.


In other words, a fractal is a mathematical object that is self-similar and chaotic. Fractals are infinitely complex: the closer you look the more detail you see. Most fractals are generated by a relatively simple equation where the results are fed back into the equation until it grows larger than a certain boundary. Most fractals are just a graph of an equation using complex numbers. The real line is the X-axis. The imaginary number line is the Y-axis. The point is fed into the equation such as the one for the Mandelbrot set.


Exhibits || Lexicon || Timeline

The Exploratorium, 1996