page_title: Percolation threshold
section_title: Thresholds for directed percolation
hierarchical_section_title: Percolation threshold / Thresholds in different dimensional spaces / Thresholds for directed percolation
caption_attribution_description: English: (2+1)D SC Lattice
context_page_description: The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component does not exist; while above it, there exists a giant component of the order of system size. In engineering and coffee making, percolation represents the flow of fluids through porous media, but in the mathematics and physics worlds it generally refers to simplified lattice models of random systems or networks, and the nature of the connectivity in them. The percolation threshold is the critical value of the occupation probability p, or more generally a critical surface for a group of parameters p₁, p₂, ..., such that infinite connectivity first occurs.
context_section_description: nn = nearest neighbors.  For a (d + 1)-dimensional hypercubic system, the hypercube is in d dimensions and the time direction points to the 2D nearest neighbors.
caption: (2+1)D SC Lattice
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