Scalar field

An example of a scalar field, with different values associated with different hues.

A scalar field is a field in which all points have a scalar value (having only magnitude). This is different from a vector field, where points have a vector value (having both magnitude and direction). Examples include temperature, pressure, humidity, and topographical maps. More formally, a mapping f such that

$\mathbf{f} : \mathbb{R}^n \rarr \mathbb{R}$