Gradient Visualizer

Visualize gradient vector fields, contour plots, and steepest ascent/descent paths

Overview

The Gradient Visualizer provides an interactive exploration of gradients, vector fields, and optimization paths in multivariable calculus. Visualize contour plots, gradient vectors, and steepest ascent/descent directions to understand how gradients point in the direction of maximum increase.

Tips

  1. Notice that gradient vectors are perpendicular to contour lines - this fundamental relationship helps you understand level curves and directional derivatives
  2. Watch gradient descent paths converge to local minima by following the negative gradient direction at each step
  3. Closer contour lines indicate steeper slopes - use the spacing to quickly identify regions of rapid change in the function
  4. Click on different starting points for gradient descent to see how the algorithm finds different local minima depending on initialization
  5. Experiment with the learning rate - too small leads to slow convergence, while too large can cause overshooting or divergence