Curse of Dimensionality: Distance Histogram & Volume Curve

Every distance-based technique in data science — k-nearest neighbors, clustering, PCA-style variance capture — quietly assumes that "near" and "far" mean something. This 2D simulator generates a real N-point cloud with d independent coordinates and shows its actual full-dimensional statistics two ways: a live histogram of sampled pairwise distances, and a pair of curves plotted against dimension itself — the exact ball/cube volume ratio (from the Gamma function) and a Monte-Carlo sweep of the relative contrast across every dimension from 2 to 150. Drag the dimension slider and watch the histogram collapse to a spike while the marker slides down both curves toward zero — no camera angle needed, because the collapse itself is the picture.