Takes a scalar field as input and produces a vector field.
Mnemonic: the gradient shows the direction in which the function increases fastest.
Think of a color gradient going from white to black from left to right.
Therefore, it has to:
  • take a scalar field as input. Otherwise, how do you decide which vector is larger than the other?
  • output a vector field that contains the direction in which the scalar increases fastest locally at each point. This has to give out vectors, since we are talking about directions