In 1880 the Italian logician Giuseppe Peano (1858-1932) constructed the Peano curve, a base motif fractal which uses a line segment as base. The motif is dividing the line segment in three parts, and making a square up and down the middle part:
This leads to a filled square, so the curve is a space-filling
1) Fractal dimension = log N / log e, where N is the number of line segments
and e the magnification.