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MaxRecursion—Wolfram Documentation

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MaxRecursion

is an option for functions like NIntegrate and Plot that specifies how many recursive subdivisions can be made.

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Examples  
Basic Examples  
Scope  
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MaxRecursion

MaxRecursion

is an option for functions like NIntegrate and Plot that specifies how many recursive subdivisions can be made.

Details

  • MaxRecursion->n specifies that up to n levels of recursion should be done.
  • Recursive subdivision is done only in those places where more samples seem to be needed in order to achieve results with a certain level of quality.
  • In d dimensions, each recursive subdivision increases the number of samples taken by a factor that increases roughly exponentially with d.
  • MaxRecursion->Infinity specifies no limit on the number of recursive subdivisions.
  • In cases such as functions with discontinuities or with infinitely rapid oscillations there may be no convergence even after an infinite number of subdivisions.

Examples

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Basic Examples  (2)

Get a very high-quality plot of a sharp feature:

Wolfram Language code: Plot3D[x y Exp[-10 (x ^ 2 + y ^ 2 - 1) ^ 2], {x, -2, 2}, {y, -2, 2}, PlotRange -> All, Mesh -> False, MaxRecursion -> 5]

Allow more adaptive recursion to resolve the integral of a rapidly varying function:

Wolfram Language code: NIntegrate[Exp[-10 ^ 8 x ^ 2], {x, -1, 1}, WorkingPrecision -> 20, MaxRecursion -> 20]

Scope  (2)

Use MaxRecursion to control adaptive subdivision:

Wolfram Language code: Table[Plot[Sin[x ^ 2], {x, 0, 10}, PlotPoints -> 5, MaxRecursion -> mr], {mr, {0, 2, 4, 6}}]
Wolfram Language code: Table[Plot3D[Sin[x y], {x, 0, 4}, {y, 0, 4}, PlotPoints -> 5, MaxRecursion -> mr, Mesh -> None], {mr, {0, 1, 2, 4}}]

Use MaxRecursion to improve results when singularities affect numerical integration:

Wolfram Language code: NIntegrate[1 / Sqrt[Sin[x]], {x, 0, 10}, MaxRecursion -> 100]

With the default setting, the result is not as good:

Wolfram Language code: NIntegrate[1 / Sqrt[Sin[x]], {x, 0, 10}]

Specifying the singularity locations is even more efficient:

Wolfram Language code: NIntegrate[1 / Sqrt[Sin[x]], {x, 0, π, 2 π, 3 π, 10}]
Wolfram Research (1991), MaxRecursion, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxRecursion.html (updated 2007).

Text

Wolfram Research (1991), MaxRecursion, Wolfram Language function, https://reference.wolfram.com/language/ref/MaxRecursion.html (updated 2007).

CMS

Wolfram Language. 1991. "MaxRecursion." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/MaxRecursion.html.

APA

Wolfram Language. (1991). MaxRecursion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaxRecursion.html

BibTeX

@misc{reference.wolfram_2026_maxrecursion, author="Wolfram Research", title="{MaxRecursion}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/MaxRecursion.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_maxrecursion, organization={Wolfram Research}, title={MaxRecursion}, year={2007}, url={https://reference.wolfram.com/language/ref/MaxRecursion.html}, note=[Accessed: 14-November-2026]}