<FractalSearch>

Fractal patterns in visual search
Deborah J. Aks

Project Overview
Objective Questions Background Experimental Design Theory	Prediction Demo tasks Data Key analyses Some results of Trial 1 to 3 search demos Future studies

Objective:

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

Questions
Many questions emerge when looking at complicated eye-movement behavior .

Here are a few...
Are there fractal patterns in visual search?
If so, what kind?
What is the significance of finding such patterns?

Background information on fractal concepts & connection to eye-movements

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 on-line tutorials related to fractals & modeling.

Mapping eye-mvmts to time-series

	-------> What's the connection? ------->


Eyeballs are modification of X. Liu's		if time series animation stops, refresh page to repeat. Credit & thanks to Frame, Mandelbrot & Neger's Yale fractal class

Key features of experimental design

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

We will minimize the stimulus role which is well known in guiding search.
Task must be sufficiently challenging to provide enough data to...
- find temporal (fractal) patterns.
- elicit wide-ranging and complex eye-movements.

Preliminary experiments & data

These data were collected by Sol Simpson of SR-Research when I was testing out their eye-trackers.

1000HZ sampling rate permits fine-resolution sampling of eye-movement 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.

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Do you notice any patterns in the eye-movements shown below?

0-----------------------Time ------------------------1.6 seconds

See mapping eye-movements to time-series

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Theory:

Most eye-movement and visual search theory is based on general linear models (GLMs) and assumes that variability across eye-movements 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. Self-organized criticality (SOC) is one such class of models that can produce complex and long-range 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 eye-movement behavior has been inspired.

Predictions

Fractal structure will emerge in scan path time series signified by scaling & self-similar properties. Furthermore, I expect to find 1/f pink noise under some (of the most unstructured) conditions on particular eye-movement 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.

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Key analyses: Statistical tests that reveal structure & correlation across eye-movements. 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)

Dependent Variables = Various parameters of eye movement behavior

listed in purple on the linked in the html & (xls) table

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Signs of fractal patterns:

noisy, complicated time series w/ frequent-small eye mvmts & rare-large mvmts
Probability Distributions (PDFs) w/ long tails
means and variance change over time
means and variance change w/ measuring resolution
non-random patterns (despite their random appearance)
statistical self-similarity
what color is the noise: white, brown, pink?
(wikipedia illustrations of noise color)
(another illustrations & ways to generate different forms of noise)

<Note: conventional theory predicts white or brown noise in eye-mvmts>
<Caution on terminology: fractal brownian motion (fbm) can include both brown & pink forms of noise;
<......fbm does not necessarily = brown (or brownian) noise >

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Future Studies will assess..

How fractal structure & scaling relations change under varying conditions
- structured vs. unstructured search
- task complexity
- gaze contingent blurring
  - central vs. peripheral
- cognitive processing load

Do temporal patterns predict...
- conventional form of memory?
  - (e.g., implicit memory, context effects)
- object binding?
  - (e.g., coherent vs. fragmented subjective contour figures)
- individual differences in search performance?
  - (e.g., what search strategies correlate w/ effective search in many real-world
    tasks such as radiology, luggage screening and satellite imagery?)

<--Fractal networks? -->
click images for enlargements

Here are 2 network representions of the html (tag) structure of this 'Fractal patterns' page

Webs as a Graph software

Node legend

$this web site as a 2nd fractal$