A fractal is a pattern which reveals reveals greater complexity when you enlarge it.

Another more detailed definition is that it is a geometrical structure which has an irregular or fragmented appearance which shows similar characteristics at all levels of magnification.

Notice the words**
fragmented** and

If you enlarge into it, you can see more clearly how it is constructed from pentagons (regular 5-sided shapes), but you still see the same basic set of shapes.

It doesn't matter how much you enlarge a normal two-dimensional geometrical figure, you will still see the same figure. If it is a three-dimensional figure, such as a cube, and you can view all the sides on a computer screen, you will still see one thing: the original cube. If you magnify it, you will merely see a larger cube. OK?

Another way of describing a fractal is to say that it is an irregular shape
that can be sub-divided into parts. Each part can look similar to the original
shape. The smaller parts are not the same: they are ** self-similar**.
In some fractals, you can see these self-similar fragments when you zoom to a
higher level of magnification. Obviously, you cannot zoom into a picture of a
fractal printed on paper. It has only two dimensions. A computer, however,
enables you to zoom in, to see fragments and parts, and in theory to continue
that process to infinity. You are moving through another sort of dimension,
perhaps.

Before we look at the Mandelbrot set, a very complex fractal, there are some simpler fractals which are worth a look.

Fractals are irregular shapes and patterns generated by algorithms, which are
arithmetical and computational formula used in a computer. They are purely
mathematical in origin. The algorithms are not designed to produce
pictures of objects in the real world. They produce fascinating and often weird
patterns and shapes which might *look like* something in the world of
nature, or even in the world of fantasy. Click below for some examples.

Dr Benoit Mandelbrot is a French mathematician. He coined the word * fractal* in
1975. That's why you won't find it in old dictionaries. It is also why there are
different definitions of it — it is a new word for a new concept.

Dr Mandelbrot based his new word on the Latin word *fractus*, which
means broken or fragmented. The Mandelbrot set, to give it its correct name, looks something like a
two-dimensional picture of a series of lakes, with decorative shore-lines. If
you zoomed into a painting of a photograph of a lake and its shores, you could
simply see larger pictures of the details. You don't see that when you zoom into
the Mandelbrot fractal on a computer screen.

When you enlarge a section of it, or zoom into part of it, you see that the patterns around the 'shores' of the 'lakes' repeat themselves change slightly. You continue zooming in, and the patterns continue to repeat and mutate, to change slightly. You seem to be able to do this for ever, but you might be limited by the capacity of your computer.

Click here to to see **
What the Mandelbrot fractal looks
like.**

**Now tackle BrainWorks before going to the
next Unit.**