Skip to main content
SpringerLink
Log in

Memory Across Eye-Movements: 1/f Dynamic in Visual Search

  • Published:
Nonlinear Dynamics, Psychology, and Life Sciences

Abstract

The ubiquity of apparently random behavior in visual search (e.g., Horowitz & Wolfe, 1998) has led to our proposal that the human oculomotor system has subtle deterministic properties that underlie its complex behavior. We report the results of one subject's performance in a challenging search task in which 10,215 fixations were accumulated. A number of statistical and spectral tests revealed both fractal and 1/f structure. First, scaling properties emerged in differences across eye positions and their relative dispersion (SD/M)—both decreasing over time. Fractal microstructure also emerged in an iterated function systems test and delay plot. Power spectra obtained from the Fourier analysis of fixations produced brown (1/f 2) noise and the spectra of differences across eye positions showed 1/f (pink) noise. Thus, while the sequence of absolute eye positions resembles a random walk, the differences in fixations reflect a longer-term dynamic of 1/f pink noise. These results suggest that memory across eye-movements may serve to facilitate our ability to select out useful information from the environment. The 1/f patterns in relative eye positions together with models of complex systems (e.g., Bak, Tang & Wiesenfeld, 1987) suggest that our oculomotor system may produce a complex and self-organizing search pattern providing maximum coverage with minimal effort.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  • Aks, D. J., Nokes, T. Sprott, J. C. & Keane, E. (1998). Resolving perceptual ambiguity in the Necker Cube: A dynamical systems approach. Abstracts of the Psychonomics Society, 3, 38.

    Google Scholar 

  • Allport, D. A. (1987). Selection-for-action: Some behavioral and neurophysiological considerations of attention and action. In H. Heuer & A. F. Sanders, (Eds.), Perspectives on Perception and Action. Hillsdale, N.J.: Erlbaum.

    Google Scholar 

  • Bak, P. (1996). How nature works: the science of self-organized criticality. (pp. 52–64) NewYork: Springer-Verlag.

    Google Scholar 

  • Bak, P., & Tang, C. (1989). Earthquakes as a self-organized critical phenomenon. Journal of Geophysics Research-Solar. Earth Planet, 94, 15635–15637.

    Google Scholar 

  • Bak, P., Tang,C., & Wiesenfeld, K. (1987). Self-organized criticality: Anexplanation of 1/f noise. Physical Review Letters, 59, 381–384.

    Google Scholar 

  • Bak, P., Tang, C., & Wiesenfeld, K. (1988). Self-organized criticality. Physical Review A, 38, 364–374.

    Google Scholar 

  • Barnsley, M. F., Devaney, B. B., Mandelbrot, H. O., Peitgen, D., Saupe, D., & Voss, R. F. (1988). The Science of Fractal Images. New York: Springer-Verlag.

    Google Scholar 

  • Bouma, H., & Bouhuis, D. G. (1984). Components of visual attention. Attention and Performance X. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Bovik, A. C., Clark, M. & Geisler, W. (1990). Multichannel texture analysis using localized spatial filters, IEEE Pattern Analysis and Machine Intelligence, 12, 55–73.

    Google Scholar 

  • Burr, D. (1980). Motion smear. Nature, 284, 164–165.

    Google Scholar 

  • Carlson-Radvansky, L. & Irwin D. (1995). Memory for structural information across eye movements. Journal of Experimental Psychology: Learning, Memory & Cognition, 21, 1441–1458.

    Google Scholar 

  • Daugman, J. G. (1991). Self-similar oriented wavelet pyramids: Conjectures about neural non-orthogonality. In A. Gorea (Ed.), Representations of Vision. (pp. 27–46) Cambridge: Cambridge University Press.

    Google Scholar 

  • Duncan, J., & Humphreys, G. W. (1989). Visual search and stimulus similarity. Pscyhology Review, 96, 433–458.

    Google Scholar 

  • Ellis, S. R., & Stark, L. (1986). Statistical dependency in visual scanning. Human Factors, 28, 421–438.

    Google Scholar 

  • Engel, F. L. (1977). Visual conspicuity, visual search, and fixation tendencies of the eye. Vision Research, 17, 95–108.

    Google Scholar 

  • Fisher, D. L., Duffy, S., Young, C., & Pollatsek, A. (1988). Understanding the central processing limit in consistent-mapping visual search tasks. Journal of Experimental Psychology: Human Perception and Performance, 14, 253–266.

    Google Scholar 

  • Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.

    Google Scholar 

  • Gilden, D. L. (1996). Fluctuations in the time required for elementary decisions. Psychological Science, 8, 296–302.

    Google Scholar 

  • Gilden, D. L., Thornton, T., & Mallon, M. (1995). 1/f noise in human cognition. Science, 267, 1837–1839.

    Google Scholar 

  • Gould, J. D. (1973). Eye movements during visual search and memory search. Journal of Experimental Psychology, 98, 184–195.

    Google Scholar 

  • Grieger, B. (1992). Quaternary climatic fluctuations as a consequence of self-organized criticality. Physica A, 191, 51–56.

    Google Scholar 

  • Groner, R., & Groner, R., (1982). Towards a hypothetico-deductive theory of cognitive activity. In R. Groner & P. Fraisse (Eds.) Cognition and EyeMovements. (pp. 100–121) Amsterdam: North Holland Publishing.

    Google Scholar 

  • Groner, R., & Groner, M. (1984). A stochastic hypothesis testing model for multi-term series problems, based on eye fixations. In R. Groner, C. Menz, D. F. Fisher, & R. A. Monty (Eds.), Eye Movements and Psychological Functions: International Views. (pp. 257–274). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Grossberg, S., Mingolla, E., & Ross, W.D. (1984). Aneural theory of attentive visual search: Interactions of boundary, surface, spatial, and object representations. Psychological Review, 101, 470–489.

    Google Scholar 

  • Hayhoe, M., Lachter, J., & Feldman, J. (1991). Integration of form across saccadic eye movements. Perception, 20, 393–402.

    Google Scholar 

  • Hilborn, R. C. (1994). Chaos and Nonlinear Dynamics: An introduction for Scientists and Engineers. Oxford: Oxford University Press.

    Google Scholar 

  • Hochberg, J. (1968). In the minds eye. In R. N. Haber (Ed.), Contemporary theory and research in visual perception. (pp. 309–331). New York: Holt, Reinhart & Winston.

    Google Scholar 

  • Horowitz, T. S. & Wolfe, J. M. (1998). Visual Search has no memory. Nature, 357, 575–577.

    Google Scholar 

  • Humphreys, G.W., Quinlan, P. T., & Riddoch, M. J. (1989). Grouping processes in visual search: Effects with single and combined-feature targets. Journal of Experimental Psychology: General, 118, 258–279.

    Google Scholar 

  • Inditsky, B., & Bodmann, H. W. (1980). Quantitative models of visual search. In Proceedings of the 19th symposium of CIE. (pp. 197–201). Paris: Commission Internationale de l'Eclairage.

    Google Scholar 

  • Irwin, D. E. (1992). Memory for position and identity across eye movements. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18, 307–317.

    Google Scholar 

  • Irwin, D. E. (1993). Memory for spatial position across saccadic eye movements. In G. d'Ydewalle & J.V. Van Rensbergen (Eds.), Perception and Cognition. (pp. 323–332)

  • Irwin D. E. (1996). Integration and accumulation of information across saccadic eye movements. In Inui, T., & McLelland, J. L. (Eds.) Attention and performance XVI: Information integration in perception and communication (pp. 125–155). London: MIT Press.

    Google Scholar 

  • Jeffrey, H. J. (1992). Chaos game visualization of sequences. Computers & Graphics, 16, 25–33.

    Google Scholar 

  • Jonides, J., Irwin, D. E., & Yantis, S. (1981). Integrating visual information from successive fixations. Science, 215, 192–194.

    Google Scholar 

  • Kelso, S. (1992). Dynamic Patterns. Cambridge: MIT Press.

    Google Scholar 

  • Klein R. (1988). Inhibitory tagging system facilitates visual search. Nature, 334, 430–431.

    Google Scholar 

  • Klein R. (1980). Does oculomotor readiness mediate cognitive control of visual attention? In R. S. Nickerson (Ed.), Attention and Performance VIII, (pp. 259–276). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Klein R. & MacInnes, W. J. (1999). Inhibition of return is a foraging facilitator in visual search. Psychological Science, 10, 346–352.

    Google Scholar 

  • Kolers, P.A. (1976). Buswell discoveries. In R.A. Monty & J.W. Sanders (Eds.), EyeMovements and Psychological Processes. (pp. 373–395). Hillsdale, N.J.: Erlbaum.

    Google Scholar 

  • Kowler, E. (1989). Cognitive expectations, not habits, control anticipatory smooth oculomotor pursuit. Vision Research, 29, 1049–1057.

    Google Scholar 

  • Kraiss, K. F., & Knaeuper, A. (1983). Using visual lobe area to predict visual search time. Human Factors, 24, 673–682.

    Google Scholar 

  • Krendel, E. S., & Wodinsky, J. (1960). Search in an unstructured visual field. Journal of the Optical Society of America, 50, 562–568.

    Google Scholar 

  • Kristjansson, A. (2000). In search of Remembrance: Evidence for memory in visual search. Psychological Science, 11, 328–332.

    Google Scholar 

  • Liebovitch, L. S. (1998). Fractals and chaos: Simplified for the life sciences. Oxford: Oxford University Press.

    Google Scholar 

  • Locher, P. J., & Nodine, C. E. (1974). The role of scanpaths in the recognition of random shapes. Perception & Psychophysics, 15, 308–314.

    Google Scholar 

  • MacKay, D. M. (1973). Visual stability and voluntary eye movements. In R. Jung (Ed.), Handbook of sensory and voluntary eye movements.Vol. VII/3A (pp. 307–331). Berlin: Springer.

    Google Scholar 

  • Mandelbrot, B. B. (1967). How long is the coast of Britain? Statistical self-similarity and Fractal Dimension. Science, 156, 636–638.

    Google Scholar 

  • Mandelbrot, B. B. (1982). The fractal geometry of nature. San Francisco: Freeman.

    Google Scholar 

  • Mata-Toledo, R. A., & Willis, M.A. (1997). Visualization of random sequences using the Chaos Game algorithm. The Journal of Systems and Software, 39, 3.

    Google Scholar 

  • Matin, L. (1972). Eye movements and perceived visual direction. In D. Jameson & L.V. Hurvich (Eds.), Handbook of Sensory Physiology, Vol VII/4 Visual Psychophysics (pp. 331–380). Berlin: Springer-Verlag.

    Google Scholar 

  • Matin, L. (1974). Saccadic supression: A review and analysis. Psychological Bulletin, 81, 899–917.

    Google Scholar 

  • Maylor, E. (1985). Facilitatory and inhibitory components of orienting in visual space. In M. I. Posner & B. B. Marin (Eds.), Attention and performance XI (pp. 189–204). Hillsdale NJ: Erlbaum.

    Google Scholar 

  • Maylor, E. A., & Hockey, R. (1985). Inhibitory component of externally controlled covert orienting in visual space. Journal of Experimental Psychology: Human Perception & Performance, 11, 777–787.

    Google Scholar 

  • McConkie, G. W. & Rayner, K. (1976). Identifying the span of the effective stimulus in reading: Literature review and theories of reading. In H. Singer & R.B. Ruddell (Eds.), Theoretical models and processes of reading. (pp. 137–162) Newark, DE: International Reading Association.

    Google Scholar 

  • Megaw. E.D. & Richardson, J. (1979). Target uncertainty and visual scanning strategies. Human Factors, 21, 303–315.

    Google Scholar 

  • Miller, S. L., Miller, W. M., & McWhorter, P. J. (1993). Extremal dynamics: A unifying physical explanation of fractals, 1/f noise and activated processes. Journal of Applied Physics, 73, 2617–2628.

    Google Scholar 

  • Miramontes, O., & Rohani, P. (1998). Intrinsically generated coloured noise in laboratory populations. Proceedings of Royal Society of London B. 265, 785–792.

    Google Scholar 

  • Monk, T. H. (1976). Target uncertainty in applied visual search. Human Factors, 18, 607–612.

    Google Scholar 

  • Motter, B. C. & Belky, E. J. (1998) Guidance of eye movements during active visual search. Vision Resarch 38, 1805–1815.

    Google Scholar 

  • Musha, T., Sato, S. & Yamamoto, M. (1991). Noise in physical systems and 1/f fluctuations. Tokyo: Ohmsha Ltd.

    Google Scholar 

  • Neisser, U. (1967). Cognitive psychology. New York: Appleton.

    Google Scholar 

  • Noton, D. & Stark, L. (1971). Scanpaths in saccadic eye movements while viewing and recognizing patterns. Vision Research, 11, 929–942.

    Google Scholar 

  • O'Regan, J. K. (1992). Solving the “real” mysteries of visual perception: The world as an outside memory. Canadian Journal of Psychology, 46, 461–488.

    Google Scholar 

  • O'Regan, J. K., & Levy-Schoen, A. (1983). Integrating visual information from successive fixations: Does trans-saccadic fusion exist? Vision Research, 23, 765–769.

    Google Scholar 

  • Paczuski, M., & Boettcher, S. (1996). Universality in sandpiles, interface depinning, and earthquake models. Physical Review Letters, 77, 111.

    Google Scholar 

  • Palmer, J. (1995). Attention in visual search: Distinguishing four cases of a set-size effect. Current directions in Psychological Science, 4, 118–123.

    Google Scholar 

  • Pashler, H. (1987). Detecting conjunctions of color and form: Reassessing the serial search hypothesis. Perception and Psychophysics, 41, 191–201.

    Google Scholar 

  • Peak, D., & Frame, M. (1994). Chaos Under Control: The Art and Science of Complexity. New York: W. H. Freeman.

    Google Scholar 

  • Peitgen, H. O., Jurgens, H., & Saupe, D. (1993). Fractals for the Classroom. NewYork: Springer-Verlag.

    Google Scholar 

  • Port, R. F. & van Gelder, T. (1995). Mind as Motion: Explorations in the dynamics of cognition. Cambridge: MIT Press.

    Google Scholar 

  • Posner, M. (1980). Orienting of attention. Quarterly Journal of Experimental Psychology, 32, 3–25.

    Google Scholar 

  • Posner M. & Cohen, Y. (1984). Components of visual attention. In H. Bouma & D.G. Bouhuis (Eds.), Attention and Performance X. Hillsdale NJ: Erlbaum.

    Google Scholar 

  • Pratt, J. (1995). Inhibition of return in a discrimination task. Psychonomic Bulletin and Review, 2, 117–120.

    Google Scholar 

  • Press, W. H., Flannery, S. A., Teukolsky, S. A., & Vetterling, W. T. (1986). Numerical Recipes. New York: Cambridge University Press.

    Google Scholar 

  • Pressing, J. (1999) The referential dynamics of Cognition and action. Psychological Review, 106, 714–747.

    Google Scholar 

  • Rayner, K. & Pollatsek, A. (1981). Eye movement control during reading: Evidence for direct control. Quarterly Journal of Experimental Psychology: Human Experimental Psychology, 33A, 351–373.

    Google Scholar 

  • Remington, R. W. (1980). Attention and saccadic eye movements. Journal of Experimental Psychology: Human Perception and Performance, 6, 726–744.

    Google Scholar 

  • Rensink, R., O'Regan, J. K. & Clark, J. J. (1997). To see or not to see: the need for attention to perceive changes in scenes. Psychological Science, 8, 368–373.

    Google Scholar 

  • Rhodes, C. J., & Anderson, R. M. (1997). Epidemic thresholds and vaccination in a lattice model of disease spread. Theory of Population Biology, 52, 101–106.

    Google Scholar 

  • Rizzolatti, G., Riggio, L., Dascola, I., & Umilta, C. (1987). Reorienting attention across the vertical and horizontal meridians: Evidence in favor of a premotor theory of attention. Neuropsychologia. 25, 31–40.

    Google Scholar 

  • Scinto, L., Pillalamarri, R., & Karsh, R. (1986). Cognitive strategies for visual search. Acta Psychologica, 62, 263–292.

    Google Scholar 

  • Shannon, C. E., & Weaver, W. (1949). The mathematical theory of communication. Urbana: University of Illinois Press.

    Google Scholar 

  • Shebilske, W. (1977). Visuomotor coordination in visual direction and position constancies. In W. Epstein (Ed.) Stability and constancy in visual perception: Mechanisms and processes (pp. 23–70). New York: JohnWiley.

    Google Scholar 

  • Shepard, M., Findlay, J. M., & Hockey, R. J. (1986). The relationship between eye movements and spatial attention. Quarterly Journal of Experimental Psychology, 38A, 475–491.

    Google Scholar 

  • Shore, D. I. & Klein, R. M. (in press). On the manifestations of memory in visual search, Spatial Vision.

  • Simons, D. J. & Levins D. (1997). Change blindness. Trends in Cognitive Science, 1, 261–267.

    Google Scholar 

  • Sprott, J. C., & Rowlands, G. (1995). Chaos Data Analyzer. Raleigh, NC: Physics Academic Sofware (American Institute of Physics).

    Google Scholar 

  • Stassinopoulos, D., & Bak, P. (1995). Democratic Reinforcement.Aprinciple for Brain function. Physical Review E, 51, 5033.

    Google Scholar 

  • Tipper, S. P., Driver, J., & Weaver, B. (1991). Object-centered inhibition of return of visual attention. Quarterly Journal of Experimental Psychology, 43A, 289–298.

    Google Scholar 

  • Townsend, J. T. (1971). A note on the identification of parallel and serial processes. Perception and Psychophysics, 10, 161–163.

    Google Scholar 

  • Townsend, J. T. (1976). Serial and within-stage independent parallel model equivalence on the minimum completion time. Journal of Mathematical Psychology, 14, 219–239.

    Google Scholar 

  • Townsend, J. T. (1990). Serial and parallel processing: Sometimes they look like Tweedledum and Tweedledee but they can (and should) be distinguished. Psychological Science, 1, 46–54.

    Google Scholar 

  • Treisman, A. (1992). Spreading suppression or feature integration? A reply to Duncan and Humphreys (1992). Journal of Experimental Psychology: Human Perception and Performance, 18, 589–593.

    Google Scholar 

  • Treisman, A., & Gelade, G. (1988). A feature integration theory of attention. Cognitive Psychology, 12, 97–136.

    Google Scholar 

  • Umilta, C. & Moskovitch, M. (1994). Space and selective attention. Attention and Performance XV (pp. 231–265). Cambridge, MA: MIT Press.

    Google Scholar 

  • Voss, R. F. (1992). Evolution of long-range fractal correlations and 1/f noise in DNA base sequences. Physics Review Letters, 68, 3805–3808.

    Google Scholar 

  • Watson, A. B. (1987). Efficiency of an image code based on human vision. Journal of the Optical Society of America, A4, 2401–2417.

    Google Scholar 

  • West, B. J. & Deering, B. (1995). The lure of modern science: Fractal thinking. Studies of Nonlinear Phenomena in Life Sciences. Singapore: World Scientific.

    Google Scholar 

  • Widdel, H. & Kaster, J. (1981). Eye movement measurement in assessment and training of visual performance. In J. Moraal & K. F. Kraiss (Eds.), Manned systems design: Methods, equipment, and applications. (pp. 251–270). New York: Plenum Press.

    Google Scholar 

  • Wolfe, J. M. (1994). Guided search 2.0: A revised model of visual search. Psychonomic Bulletin & Review 1, 202–238.

    Google Scholar 

  • Wolfe, J. M. (1998). Visual search. In H. Pashler (Ed.), Attention, (pp. 13–71). London: University College London Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Psychology, University of Wisconsin – Whitewater, Whitewater, WI

    Deborah J. Aks

  2. Department of Psychology, State University of New York, Stony Brook, NY

    Gregory J. Zelinsky

  3. Department of Physics, University of Wisconsin – Madison, Madison, WI

    Julien C. Sprott

Authors
  1. Deborah J. Aks
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gregory J. Zelinsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Julien C. Sprott
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aks, D.J., Zelinsky, G.J. & Sprott, J.C. Memory Across Eye-Movements: 1/f Dynamic in Visual Search. Nonlinear Dynamics Psychol Life Sci 6, 1–25 (2002). https://doi.org/10.1023/A:1012222601935

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012222601935

Search

Navigation