Mean-Shift Clustering: Climbing the Density Landscape

This simulator turns a scatter of 2D data into a live 3D terrain: height at every point is the kernel density estimate of the data, so clusters appear as hills and the gaps between them as valleys. Mean shift then lets every data point climb that terrain — on each iteration a point moves to the weighted mean of its neighbours under a Gaussian kernel, which is exactly gradient ascent on the density surface. Points that converge on the same peak are merged into one cluster and colour-coded together, with no cluster count chosen in advance. A bandwidth slider reshapes the terrain in real time from many sharp peaks to one broad hill, making the algorithm's core bias/variance trade-off directly visible, while live readouts track iteration count, discovered cluster count, and the shrinking average step size as the system converges.