# Generation of percolation cluster perimeters by a random walk

@article{Ziff1984GenerationOP, title={Generation of percolation cluster perimeters by a random walk}, author={Robert M. Ziff and Peter T. Cummings and G. Stells}, journal={Journal of Physics A}, year={1984}, volume={17}, pages={3009-3017} }

A type of self-avoiding random walk whish generates the perimeter of two- dimensional lattice-percolation clusters is given. The algorithm has been simulated on a computer, yielding the mean perimeter length as a function of occupation probability.

## 83 Citations

### Percolation and self-avoiding random loops

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- 1991

Presents simulations supporting the conjecture that properly defined exterior perimeters of 2D critical percolation clusters have the same fractal dimension, D=4/3, as self-avoiding random walks. In…

### Structure of backbone perimeters of percolation clusters

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- 1989

The author studies perimeters of backbones of percolation clusters at the percolation threshold in two dimensions. These perimeters are self-avoiding for all lattices. They simulate these perimeters…

### COMMENT: On the hull of two-dimensional percolation clusters

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- 1986

A recently proven equivalence between certain random walks with memory and the hull of percolation clusters in two dimensions is used to estimate the fractal dimension of the latter by means of Monte…

### Scaling behaviour of cluster hulls in spiral site percolation

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- 1993

The scaling behaviour of the percolation hull rotationally constrained site percolation on the square and triangular lattices is studied. The single cluster growth method has been used to determine…

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- 1987

The indefinitely growing self-avoiding walk is solved exactly on a regular fractal, the Sierpinski gasket. The fractal dimension D=In 5/In 2-1 differs from the value of D for the equilibrium…

### New universality classes in “Percolative” dynamics

- Physics
- 1991

We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of…

### The efficient determination of the percolation threshold by a frontier-generating walk in a gradient

- Physics
- 1986

The frontier in gradient percolation is generated directly by a type of self-avoiding random walk. The existence of the gradient permits one to generate an infinite walk on a computer of finite…

### Structure and perimeters of percolation clusters

- Physics
- 1986

Site percolation clusters are simulated at the percolation threshold on the square lattice. An algorithm for walks around each cluster is used to obtain information on its fractal geometry. The…

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