Correlation Dimension (Grassberger-Procaccia 1983)

Estimate the fractal dimension of a strange attractor from a time series, without knowing the underlying equations.

D₂ = ?
GP algorithm: C(r) = #{pairs: |xᵢ-xⱼ|<r}/N² ~ r^D₂. Slope of log C vs log r gives D₂.
Attractor (projected)
Correlation integral C(r) — log-log
Estimated D₂:
Known value:
Scaling range:
Local slope d(log C)/d(log r) — plateau indicates fractal dimension
Click "Compute D₂" to estimate the fractal dimension.