We solve for the internal structure of $d$-dimensional percolation clusters. We find that if we randomly choose two points, then the backbone connecting these two points can be described as a randomly constructed "necklace" whose building blocks are $s$-site volatile fractals (they are not stable under a length scale change). We find the blob-size distribution function and calculate the relevant parameters numerically, thereby obtaining the first accurate estimates for the fractal dimension of the backbone in $d=2,3\mathrm{}$.

• Received 26 June 1984

DOI:https://doi.org/10.1103/PhysRevLett.53.1121