laplacian

The Laplacian is a mathematical operator that measures how a quantity, like heat, pressure, or elevation, changes around a specific point compared to its surroundings. Essentially, it looks at the difference between a point’s value and the average of nearby points, helping us understand whether the quantity is increasing or decreasing locally. It’s widely used in fields like physics, engineering, and image processing to analyze patterns, smooth data, or solve complex differential equations. In simple terms, the Laplacian provides insight into the "curvature" or "spread" of data around a location.