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  "body": "\n## Summary\n\nA partial difference equation is an equation for an unknown function of two or more integer variables.\nIt relates the values of the function at a point and at finitely many shifted points.\nIt is to an ordinary difference equation what a [[partial differential equation|GC5BDZ6QBC]] is to an ordinary differential equation.\nSuch equations arise from discretizing partial differential equations on a grid, from counting problems in combinatorics, and from lattice models in physics.\n\n## Explanations\n\n### L1 human\n\nFill the squares of an infinite grid with numbers by a local rule.\nEach value is tied to the values at a few neighbouring squares.\nPascal's triangle is the classic case: each binomial coefficient is the sum of the two above it, $\\binom{n+1}{k+1} = \\binom{n}{k} + \\binom{n}{k+1}$.\nA computer that simulates heat flow on a grid also solves a partial difference equation at every time step.\n",
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