Fractal Mechanisms in Neural Control

[claude]

http://www.physionet.org/tutorials/fmnc/index.shtml

Fractal Mechanisms in Neural Control
Human Heartbeat and Gait Dynamics in Health and Disease
 
    Introduction
    Fractal Analysis Methods
        Fractal Objects and Self-Similar Processes
        Mapping Real-World Time Series to Self-Similar Processes
        Detrended Fluctuation Analysis (DFA)
        Relationship Between Self-Similarity and Auto-Correlation Functions
    Fractal Dynamics of Human Heartbeat
        Is the Healthy Human Heartbeat Fractal?
        Does Fractal Scaling Break Down in Disease and Aging?
        Clinical Utility of Fractal Heart Rate Analysis
    Fractal Dynamics of Human Walking
        Is Healthy Gait Rhythm Fractal?
        Stability of Healthy Fractal Rhythm: Effects of Walking Rate
        Mechanisms of Fractal Gait
        Alterations of Fractal Dynamics with Aging and Disease
    Fractal Dynamics of Heart Rate and Gait: Implications and General Conclusions
    References

[Chillheimer]

Also: balance when standing shows fractal patterns.

[claude]

I had hoped to use the detrended fluctuation analysis in place of correlation exponent calculations for analysing iterated function system fractal dimension, but it failed miserably (ended up with near 0.5 no matter the transforms which is the same as the white noise that controls the chaos game).  Is a pity, because DFA is O(n log n), much faster than CE's O(n^2).  I attached my implementation with some coloured noise sources as input, here's the output:

Code:

white   0.490273
brown   1.504954
violet  0.009767
pink    1.078109
blue    0.081371
black   1.934080