The simplest fractals are constructed by iteration. For
example, start with a filledin triangle and iterate this process: 
For every filledin triangle, connect the midpoints of the sides and
remove the middle triangle. Iterating this process produces, in the limit, the
Sierpinski Gasket. 

Click the picture to iterate. 

The gasket is selfsimilar.
That is, it is made up of smaller copies of itself. 

We can describe the gasket as made of three copies, each
1/2 as
tall and 1/2 as wide as the original. But note a consequence of selfsimilarity: each
of these copies is made of three still smaller copies, so we can say the gasket is made
of nine copies each 1/4 by 1/4 of
the original, or 27 copies each 1/8 by 1/8, or ... .
Usually, we prefer the simplest description. 


"Big gaskets are made of little gaskets, 
The bits into which we slice 'em. 
And little gaskets are made of lesser gaskets 
And so ad infinitum." 

This implies fractals possess a scale ambiguity. 