 Strange attractors also are often characterized as possess noninteger or fractal dimension (though not all strange attractors have such dimensionality). The type of dimensionality we usually meet in physics as well as in everyday experience is characterized by integers. A point has dimension zero; a line has dimension one; a square has dimension two; a cube has dimension three and so on. As a generalization of our intuitions regarding dimensionality, consider a large square. Suppose we fill this large square with smaller squares each having an edge length of \(\varepsilon\). The number of small squares needed to completely fill the space inside the large square is \(N(\varepsilon)\). Now repeat this process of filling the large square with small squares, but each time let the length \(\varepsilon\) get smaller and smaller. In the limit as \(\varepsilon\) approached zero, we would find that the ratio \(\ln N(\varepsilon)/\ln(1 / \varepsilon)\) equals two just as we would expect for a 2-dimensional square. You can imagine the same exercise of filling a large 3-dimensional cube (a room, say) with smaller cubes and in the limit of \(\varepsilon\) approaching zero, we would arrive at a dimension of three. 