A fast percolation simulator for an arbitrarily sized 2d grid.

Percolation theory studies how connected clusters form in a grid as random sites are occupied. This theory is essential for understanding phenomena like fluid flow in porous materials and the spread of diseases. A key focus is the percolation threshold: the critical point at which an infinite cluster appears, marking a phase transition from low to high connectivity.

• Traditional

  • Traditional percolation simulations are slow because they evaluate the entire lattice afresh for each probability step.

• Newman-Ziff

  • The Newman-Ziff algorithm ( "M. E. J. Newman and R. M. Zif. A fast monte carlo algorithm for site or bond percolation. Phys. Rev. Lett., 85:4104, Nov 2000.") enhances efficiency by incrementally occupying sites and updating

  • clusters without recalculating previous results. Its advantages include:

    • Incremental Updates:
      • Starts with an empty lattice and adds one site at a time, using previous data to avoid redundant calculations.
    • Efficient Clustering:
      • Utilizes an advanced data structure to manage cluster updates quickly, facilitating rapid checks for percolation.
    • Statistical Efficiency:
      • Computes properties for all probabilities in a single simulation, yielding high-precision results with fewer computations.

  • This repo provides a Python implementation of the fast Newman-Ziff algorithm that calculates the percolation threshold for an arbitrarily-sized 2D grid.

• Details of the implementation are described here

    ...
    ...perc_value = 0.600475
    ...perc_value = 0.5849
    ...perc_value = 0.59185
    ...perc_value = 0.58535
    ...perc_value = 0.58995
    ...perc_value = 0.586175
    ...perc_value = 0.5989
    ...perc_value = 0.590425
    ...perc_value = 0.574925
    ...perc_value = 0.623675
    ...perc_value = 0.583475
    ...average p: 0.5917819999999999 with (200x200) grid, 50 iterations in 38.44 secs 

• For detailed setup, usage, and automated tests, see here