Use koch snowflake as an example.

The Koch curve has an infinite length because each time the steps above are performed on each line segment of the figure there are four times as many line segments, the length of each being one-third the length of the segments in the previous stage. Hence the total length increases by one third and thus the length at step *n* will be (4/3)n of the original triangle perimeter: the fractal dimension is log 4/log 3 ≈ 1.26.

So for example you could create a fractal that creates 7 new line segments at each iteration with each new line segment being 1/4 the length of the original.