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Perlin noise
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==Complexity== For each evaluation of the noise function, the dot product of the position and gradient vectors must be evaluated at each node of the containing grid cell. Perlin noise therefore scales with complexity [[Big O notation|{{math|''O''(2<sup>''n''</sup>)}}]] for {{mvar|n}} dimensions.<ref>{{Citation |last1=Blatz |first1=Michael |title=A Very Short History of Dynamic and Procedural Content Generation |date=2017 |work=Game Dynamics: Best Practices in Procedural and Dynamic Game Content Generation |pages=1β13 |editor-last=Korn |editor-first=Oliver |url=https://link.springer.com/chapter/10.1007/978-3-319-53088-8_1 |access-date=2025-03-17 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-53088-8_1 |isbn=978-3-319-53088-8 |last2=Korn |first2=Oliver |editor2-last=Lee |editor2-first=Newton|url-access=subscription }}</ref> Alternatives to Perlin noise producing similar results with improved complexity scaling include [[simplex noise]] and [[OpenSimplex noise]].
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