Definition:Contour Plot

Definition

Let $f: \R^2 \to \R$ be a real function of $2$ variables.

A contour plot is a diagram in the Cartesian plane $\CC$ in which points in $\CC$ with the same values of $f$ are joined by curves for a selection of some specific values

Contour Line

Consider a contour plot of a real function $f$ of $2$ variables.

Each of the curves joining points with the same values under $f$ are known as contour lines.

Examples

Arbitrary Example

This is a contour plot of the real function $f$ of $2$ variables defined as:

$\forall x, y \in \R^2: \map f {x, y} = 4 x^2 - \dfrac {21 x^4} {10} + \dfrac {x^6} 3 + x y - 4 y^2 + 4 y^4$

for various values of $f$ between $-0 \cdotp 8$ and $10$.

Also see

• Results about contour plots can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): contour plot
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): contour plot