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 $d=2,3$.
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Herrmann et al. (1984) studied this question.
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