More specifically, a geometric fractal is formed of parts, which, when magnified, are the same as the original shape. Fractals can also involve randomness, so that the similarity of parts to the whole can be of a statistical or average property. Place them so they would make an equilateral triangle with the removed segment. Repeat this procedure with each of the line segments that now make up the curve.
Fractals get their name because they can be seen to have fractional dimension.
Length, area and volume measure the size of one, two and three dimensional shapes respectively. However, a Koch curve can be shown to be infinite in length and to cover no area. This means that if we use a ruler to measure the length of the curve, the length we find depends on how long the ruler is. The shorter the ruler, the longer is the length we measure. An example of a fractal-like shape found in nature is a coastline.