Gradients are one of the most important concepts in calculus and machine learning, but it’s often poorly understood. Trying to understand them better myself, I wanted to build a visualization tool that helps me develop the correct mental picture of what the gradient of a function is. I came across GistNoesis/VisualizeGradient, so I went on from there to write my own iteration. This mental model generalizes beautifully to higher dimensions and is crucial for understanding optimization algorithms. 2D Gradient Plot: The colored surface shows function values. Black arrows show gradient vectors in the input plane (x-y space), pointing toward the direction of steepest ascent. The colored surface shows function values. Black arrows show gradient vectors in the input plane (x-y space), pointing toward the direction of steepest ascent.

If you are interested in having a closer look or replicating my approach, the full project can be found on my GitHub. I’m also looking forward to doing something similar on the Central Limit Theorem as well as doing a short tutorial on plotting options volatility surfaces with python, a project I have been waiting to finish for some time now.