The fractal dimension of the minimum path in two-and three-dimensional percolation

@inproceedings{Hans1988TheFD,
  title={The fractal dimension of the minimum path in two-and three-dimensional percolation},
  author={Hans and Herrmannt and Harry Eugene Stanley},
  year={1988}
}
We calculate the fractal dimension d, , , of the shortest path I between two points on a percolation cluster, where 1 rd”n and r is the Pythagorean distance between the points. We find d , , ,= 1.130*0.002 for d = 2 and 1.34i0.01 for d =3 . What is the length 1 of the shortest path or ‘chemical distance’ between two points of a random material? In general, I is greater than r, the Pythagorean distance between the points. If the object is self-similar (‘fractal’) on length scales r < 6 (where 6… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 16 extracted citations

References

Publications referenced by this paper.
Showing 1-2 of 2 references

J. Phys. A: Math. Gen Phys. Rev. Lett. Phys. Rev. B J. Phys. A: Math. Gen. Phys. A: Math. Gen. IO L169 Stanley H J. Phys. A: Math. Gen. J. Phys. A: Math. Gen

  • H J Herrmann, Hong D C Stanley, H E 17 L Herrmann, H J, Stanley H Kerstein, A Edwards
  • J. Phys. A: Math. Gen Phys. Rev. Lett. Phys. Rev…
  • 1977

J. Phys. A: Math. Gen. J. Phys. A: Math. Gen. J. Phys. A: Math. Gen. Math. Biosci. Phys. A: Math. Gen. J. Phys. A: Math. Gen. Phys. B

  • B Edwards, A Kerstein
  • J. Phys. A: Math. Gen. J. Phys. A: Math. Gen. J…
  • 1681

Similar Papers

Loading similar papers…