Zoom in around one point. The spacing of its neighbours tells us how quickly the local volume fills.
Tⱼ is the distance to neighbour j; Tₖ is the neighbourhood radius.
Choose a neighbourhood.Sort the distances from the selected point to its k nearest neighbours.
Measure relative spacing.Compare each inner radius with the outer radius through log(Tₖ / Tⱼ).
Invert and aggregate.Estimate each point locally, then take the arithmetic mean of the valid estimates.
The plot is a view of the data. Distances, angles and covariance are computed in all generated coordinates. Noise, sampling and scale can change an estimate; the underlying noiseless manifold is only a reference.