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Mathematica > Visualization and Graphics > Graphics Options & Styling > Plotting Options >

Built-in Mathematica Symbol

MaxRecursion

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

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.

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

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

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

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

Use MaxRecursion to control adaptive subdivision:

Use MaxRecursion to improve results when singularities affect numerical integration:

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

Specifying the singularity locations is even more efficient: