How to read a contour map

A level curve is a slice of the surface z=f(x,y)z=f(x,y) at one fixed height.

Every point on a single contour gives the same output value, even though the coordinates are different.

Regions where contours bunch together represent steeper change, while wider spacing indicates a flatter surface.

Function input notes

  • Use standard expressions such as x2+y2x^2+y^2, x2y2x^2-y^2, or sin(x)+cos(y)sin(x)+cos(y).
  • Keep the plot window in a range where the function stays real-valued.
  • Increase contour count for finer structure, but reduce it again if labels become hard to scan.