Extended Data Figure 4: Patterson function of a disordered lattice.

A distorted lattice (left, black circles, with ideal positions in grey), with vectors (red arrows) connecting all lattice points that have difference vectors a_n −a_k = (1, 1). On the right, the arrows from the left panel are translated in two ways: upper right, the heads and tails are both displaced from their ideal positions; bottom right, the tails are lined up, resulting in the distribution of head positions forming a broader Gaussian. In the limit of a large crystal, the resultant distribution is the autocorrelation of the displacement distribution. This process can be repeated for all difference vectors, leading to equation (3).