Henon Map and Correlation Dimension

This MATLAB script simulates the Henon map, a chaotic dynamical system and computes its correlation dimension.

This MATLAB script simulates the Henon map, a classic example of a two-dimensional chaotic dynamical system. It generates the trajectory of the map in phase space, then computes the correlation dimension of the attractor. The script

• Iterates the Henon equations to produce a time series
• Computes pairwise distances between all trajectory points
• Estimates the correlation integral C(r) over a range of scales r
• Fits the power-law region of the log⁡C(r)\log vs log⁡r\log plot to extract the correlation dimension, a measure of the fractal structure of the attractor
• Visualizes both the attractor and the scaling behavior on log-log axes

This gives insight into the fractal geometry and dimensionality of the chaotic Henon attractor.