Fractal patterns
in visual search
Deborah J. Aks
Project Overview 

Study the 'internal' process guiding search by examining search patterns over time. 
Questions 

Yale's introductory Fractal
Geometry course, sponsored by Michael
Frame, Benoit Mandelbrot & Nial
Neger, has excellent demos of many fractal concepts and
analyses used to detect fractals. MIT course: Random Walks and Diffusion by Martin Bazant contains more advanced math background w/ a focus on brownian motion. Here are some additional online tutorials related to fractals & modeling. 

Mapping eyemvmts to timeseries

To evaluate whether there are fractal patterns in eyemovements, experiments are designed to optimize our ability to capture
the 'internal' search process by having the following features in our search tasks: 

Preliminary experiments & data 
These data were collected by Sol Simpson of SRResearch when I was testing out their eyetrackers. 1000HZ sampling rate permits fineresolution sampling of eyemovement patterns: In just over 3 minutes we collected ~200K data pts ! Importantly, even within such a brief period, many interesting search patterns emerge. Here's an overview of the 3 trial's data, timing & video samples of the demo search tasks. 


Most eyemovement and visual search theory is based on general linear models (GLMs) and assumes that variability across eyemovements and experimental trials is random (or due to random sampling from uniform gaussian or poisson distributions). The failure to recognize that many processes are not best described by normal distributions may be one of the most overlooked yet essential property of behavioral phenomena. Given the ubiquity of fractal patterns being discovered in nature, I expect, through the use of appropriate statistical tools to uncover search patterns with complex fractal dynamics. Moreover, finding these patterns may guide biologically plausible models such as those that include the compelling notion that visual search can be guided by simple threshold and neuronal interaction rules. Selforganized criticality (SOC) is one such class of models that can produce complex and longrange dynamics. It is described in some of our earlier preliminary work exploring these ideas in the context of human perception. SOC lies within the cellular automata (CA) framework from which this theoretical perspective on eyemovement behavior has been inspired. 
Fractal structure will emerge in scan path time series signified by scaling & selfsimilar properties. Furthermore, I expect to find 1/f pink noise under some (of the most unstructured) conditions on particular eyemovement parameters. My rationale for this prediction relates to the similarity of processes that can produce 1/f patterns and known properties of sensory/perceptual neural interactions. 
Key analyses: Statistical tests that reveal structure & correlation across eyemovements. See also signs of fractal patterns 

Probability Distributions (PDFs): >  Skew & Kurtosis 
Power spectra (FFT) >  Autocorrelation (Tau) 
Rescaled Range Analyses: >  Hurst exponent (H) 
Iterated Function Systems (IFS)  Detrend Fluctuation Analysis (DFA) 

Future
Studies will
assess.. 


<Fractal
networks? > 
Updat10/23/06
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