Level set

A level set of a function is the set of all the points where the function has a given value. This is a special application of a scalar field.

Level Set Media

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  Intersections of a co-ordinate function's level surfaces with a trefoil knot. Red curves are closest to the viewer, while yellow curves are farthest.

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  Log-spaced level curve plot of Himmelblau's function

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  Consider a function f whose graph looks like a hill. The blue curves are the level sets; the red curves follow the direction of the gradient. The cautious hiker follows the blue paths; the bold hiker follows the red paths. Note that blue and red paths always cross at right angles.