Rafa Irizarry has created GIFs to illustrate k-means clustering and LOESS regression.  See them at Simply Statistics:

• K-means
• LOESS

No associated descriptions of k-means and LOESS so if you don’t know what those methods are then do a little background reading before checking out his GIFs.

Links:

• Cleveland’s 1979 paper, “Robust Locally Weighted Regression and Smoothing Scatterplots”
• Cleveland and Devlin’s 1988 paper, “Locally Weighted Regression:  An Approach to Regression Analysis by Local Fitting”