1. Long-range fractal dynamic in visual search & beyond Deborah J. Aks UW-Whitewater Department of Psychology 4/25/05 (Presented at Rutgers University, Newark - Psychology Dept)

3. Scale-free --> Rethinking what we study & measure Typical scale = Central tendency Power laws! Many # # Few Small Large Size Size (of an event, object or behavior)

4. Some of my ‘statical’ research • Depth effects on visual search • ~1989-1997 • shading • texture gradient • isoluminant gradients • aerial perspective • height-in-plane

5. Find small (red) object

8. Horowitz, T.S. & Wolfe, J. M. (1998). VisualSearch has no memory. Nature, 357, 575-577. Do we keep track of where we look? Finding: Random repositioning of stimuli does not affect search RTs No memory?

9. Temporal dynamics in perception Task requirement:Subject needs to sustain for extended periods of time under a fixed condition! • Simple RT tasks • Perceptual reversals • Visual search

10. Overview of dynamical study • Visual search study • Power law results & implications • Possible source of 1/f results:SOC model • Future research

11. Find: Visual Search:

17. Non-systematic eye-movements especially in unstructured environments Engle, 1977; Ellis & Stark, 1988; Scinto & Pillalamarri, 1986; Krendel & Wodinsky, 1960; Groner & Groner, 1982

18. Our eye-movement study Collaborators Gregory ZelinskySUNY- Stonybrook Julien C. SprottUW-Madison Aks, D. J. Zelinsky G. & Sprott J. C. (2002). Memory Across Eye-Movements: 1/f Dynamic in Visual Search. Nonlinear Dynamics, Psychology and Life Sciences, 6 (1), 1-15.

19. QUESTIONS. • What guides complicated eye movements? • Random or non-random process? • Is there memory across fixations? • Might neural interactions drive search? • METHOD OF TESTING. • Challenging visual search task

20. Key Analyses • Descriptive & Correlational Statistics • Probability Distributions • Power spectra (FFT)

21. Visual Search Task Find the upright “T” T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T T

22. Method. • Each trial contained 81 Ts. • 400 trials lasting 2.5hours. • Eight 20-minute sessions separated by 5-minute rest • Generation V dual purkinje-image (DPI) tracker

23. Map trajectory of eyes: • Duration & x,y coordinates for each fixation.---------------------------------------------------------- • Differences between fixations • xn – xn+1 &yn – yn+1 • Distance =(x2 + y2)1/2 • Direction = Arctan (y/x).

24. Results Conventional search stats… What’s the central tendency? • 24 fixations per trial (on average) • 7.6 seconds (SD =6.9 sec) per trial • Mean fixation duration = 212 ms (SD = 89 ms) Focusing on the dynamic… • 10,215 fixations across complete search experiment.

25. Series of Fixation Differences (yn+1- yn)

26. Eye Fixations Scatter plot of 10,215 eye fixations for the entire visual search experiment.

27. Delay Plot of Fixations yn-vs- y n+1

28. Across 8 sessions we see scaling : • Fixation frequency decreased from 1888 to 657 • Fixation duration increased from 206 to 217 ms. • Changes in fixation position … • xn – xn+1 decreased • yn – yn+1 increased No typical scale!

29. Heavy-tail distributions • Power-laws • Small changes are common; large ones are rare! xn - x n+1

30. Heavy-tail distributions • Small changes are common; large ones are rare! yn- y n+1

31. Spectral analysis Fast-Fourier Transform (FFT) Power vs. Frequency Regression slope = power exponent f a f -2 = 1/ f 2 Brown noise

32. Noisy time series White Pink Brown

33. 1/f 0 noise -- flat spectrum= no correlation across data points Short & Long range = 0 White Noise Pink Noise 1/f noise --shallow slope = subtle long range correlation 1/f 2 noise-- steep slope = Predictable long-range, ‘undulating’ correlation Short range = 0 (successive events uncorrelated) Brown Noise

34. Power law indicates… • Memory • Steepness of the slope (on a log-log scale) reflects.. • Correlation across data points = ‘Colored’ noise • White • Pink • Brown • Fractal properties: • Scale-free (means  w/ measuring resolution) • Self-similar (statistically) • Critical + flexible + self-organizing (1/f)

35. PowerSpectra on raw fixations 

36. PowerSpectra of first differences across fixations  = -.6

37. Distance across eye fixations (x2 + y2) 1/2  = -.47

38. Summary of results: • Sequence of… • Absolute eye positions --> 1/f brown noise • No short-term memory; Predictable long-term memory • Differences-across-fixations --> 1/f pink noise • Subtle long-term memory.

39. Overview of dynamical study • Visual search study • Power law results & implications • Possible source of 1/f results:SOC model • Future research

40. Power laws are common Newman, M. (2005). Power laws, Pareto distributions and Zipf’s laws. Physics Letters, 2.

41. Heavy-tail distributions • Power-laws • Small changes are common; large ones are rare! xn - x n+1

42. Network ---> Distribution Barabasi, A. & Bonabeau, E. (2003). Scale-Free Networks. Scientific American, 288, 60-69.

44. Edelman, G. & Tononi, G. (2000).A Universe of Consciousness: How Matter Becomes Imagination..

45. Scale-free brain functional networksV. M. Eguíluz et al., (2005). Phys. Rev. Lett. 92, 028102

46. Scale-free brain functional networksV. M. Eguíluz et al., (2005). Phys. Rev. Lett. 92, 028102

47. Overview of dynamical study • Visual search study • Power law results & implications • Possible source of 1/f results:SOC model • Future research

48. PowerSpectra of first differences across fixations  = -.6

49. Source of 1/f dynamic? (Big controversy!)

50. Model ~ Hebb, 1969; Rummelhardt & McClelland, 1985 Grossberg et al, 2003 Neuronal interactions ---> implicit guidance Can eye movements be described by a simple set of neuronal interaction rules (e.g., SOC) to produce 1/f behavior?