Fundamentals

The gradient points in the direction of the steepest increase of the scalar field (e.g. height, temperature). It tells you:

• Where to go to climb fastest uphill

• How steep that climb is

  
  

  Example: On a temperature plate, the gradient shows where it gets hotter most quickly.

The divergence of a gradient (also called the Laplacian) tells you whether a point is higher or lower than its surroundings. It measures the curvature of the field at a point.

• Positive: local valley (value lower than surroundings)

• Negative: local hilltop (value higher than surroundings)

  
  

  Example: On a landscape, it tells you if you're on a peak, in a pit, or on flat terrain.

It represents the Laplacian and is derived using the divergence of the gradient.