rate of change of a quantity across space or along a dimension
mathematically: vector of partial derivatives pointing in the direction of steepest increase
temperature gradients drive heat flow (Fourier's law)
concentration gradients drive diffusion (Fick's law)
pressure gradients drive fluid flow
electrochemical gradients across cell membranes power ATP synthesis and nerve impulses
altitude gradients shape climate zones, vegetation bands, and species distribution
gradient descent: optimization algorithm that follows the negative gradient to minimize a loss function
central to machine learning, thermodynamics, fluid dynamics, and ecology