percolationtype

Percolationtype is a designation used in percolation theory to describe the rule by which the basic units of a system are occupied and connected. In standard lattice models, the most common percolation types are site percolation and bond percolation. In site percolation, each lattice site is independently occupied with probability p; bonds connect neighboring sites, and clusters form by occupied sites that are connected through those occupied neighbors. In bond percolation, all sites are present, but each bond (edge) between neighboring sites is kept with probability p; clusters form through sequences of present bonds. The percolationtype determines how connectivity and cluster statistics are defined, and it affects the critical occupation probability p_c at which a spanning cluster first appears in the limit of infinite system size. For example, on a two-dimensional square lattice, p_c is about 0.5927 for site percolation and 0.5 for bond percolation. Mixed or more complex rules, such as bootstrap percolation, directed percolation, or continuum percolation, are sometimes grouped under the broader umbrella of percolation types in specialized studies.

In practice, percolationtype serves as a label in simulations and mathematical treatments to distinguish different occupancy rules and their implications for connectivity, phase transitions, and scaling behavior. The concept is central to applications in materials science, epidemiology, network robustness, and flow in porous media, where the emergence of a large-scale connected structure governs macroscopic properties.