Famous Fractals   

Hilbert Curve

The Hilbert Curve is a fractal that can be formed using the following l-system:

Hilbert {
Angle 90
Axiom X
X = –YF+XFX+FY–
Y = +XF–YFY–FX+
}

With increasing number of iterations, it is formed the following way:

As you can see, the fractal fills a square, which means that it is a Peano curve.

FRACTAL DIMENSION
Since the Hilbert Curve is a Peano curve, its fractal dimension must be 2.

LENGTH
At every iteration, the fractal becomes 2 units longer. After an infinite number of iterations, it becomes infinitely long, just like all fractal curves do.