Gaussian Mixture Models: EM Density Contours in 2D

This is the flat, native-2D counterpart of the 3D Gaussian Mixture Model simulator. It runs the same Expectation-Maximization algorithm — every component owns a full 2D covariance ellipse, not just a centroid, and every point carries a soft probability of belonging to each one — but visualises the resulting mixture density as a colour-banded contour map drawn straight onto the canvas, the way a topographic map encodes elevation without ever tilting the view. Log-likelihood, its step-to-step change, and the mean responsibility entropy are read out numerically so you can watch the algorithm provably climb toward a local optimum and settle.