Fig. 1.
The measured dimensionality of a long pipe. (A) Schematic representation of the scaling of the correlation function with distance; the number of points within a distance r scales as rD. (B) Correlation function for 100,000 points randomly distributed so as to define a hollow tube of length unity. The radius of the tube is 10−2 and the thickness of the tube wall 10−4. The slopes give dimensions of 3.0, 2.0, and 1.0, respectively, at length scales that are smaller than the thickness of the wall, between the thickness of the wall and the diameter of the tube, and longer than the diameter of the tube.