Generate contour (level curve) maps for z=f(x,y) with adjustable levels, color fills, and gradient vectors.
Enter a function z=f(x,y), choose an x-y viewing window, and select the z-values to draw as contours. The plotter can distinguish ranges between contours with color fills and overlay gradient vectors that indicate the direction of increasing function value. Each contour is a level set f(x,y)=c projected onto the x-y plane, not a three-dimensional path. A common mistake is treating filled color bands as additional contour lines. Each band represents values between adjacent selected levels.
A concrete input and expected output from the current implementation.
Input
Function: x^2 + y^2 x range: -2 to 2 y range: -2 to 2 Contour level: 1
Expected output
The map contains one closed contour: the unit circle x^2 + y^2 = 1, centered at (0,0). It crosses the axes at (1,0), (-1,0), (0,1), and (0,-1).
A level-1 contour contains exactly the points where the function equals 1. For x^2 + y^2, that equation describes a circle with radius 1.
For every requested value c, the plotter draws the x-y locations satisfying f(x,y)=c within the chosen window. Closed contours can surround peaks, valleys, or other regions, while open contours continue to a plot boundary. Changing the level list changes which function values are traced; changing the viewing window can clip or reveal additional branches of the same level set.
Color fills separate value intervals bounded by the selected contour levels. Gradient vectors represent the local direction in which f increases most rapidly. Where f is differentiable and its gradient is nonzero, those vectors are perpendicular to the level curve through the same point. Arrow direction does not show movement along a contour, since f remains constant along that curve.
No. It shows selected function values as curves in the x-y plane. Color fills can communicate value ranges, but they do not provide perspective or surface height. Use a three-dimensional surface plot when you need to inspect overhang-free shape, viewing angle, or apparent vertical relief directly.
For a differentiable function, the gradient is normal to a smooth level curve wherever the gradient is nonzero. It therefore crosses the contour rather than following it and points toward increasing values. At stationary points the gradient is zero, so no preferred arrow direction exists. This relationship can also fail where the function is not differentiable.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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