Sequences of predictive eye movements form a fractional Brownian series--implications for self-organized criticality in the oculomotor system

On Relationships Between Fixation Identification Algorithms and Fractal Box Counting Methods

Fixation identification algorithms facilitate data comprehension and provide analytical convenience in eye-tracking analysis. However, current fixation algorithms for eye-tracking analysis are heavily dependent on parameter choices, leading to instabilities in results and incompleteness in reporting. This work examines the nature of human scanning patterns during complex scene viewing. We show that standard implementations of the commonly used distance-dispersion algorithm for fixation identification are functionally equivalent to greedy spatiotemporal tiling. We show that modeling the number of fixations as a function of tiling size leads to a measure of fractal dimensionality through box counting. We apply this technique to examine scale-free gaze behaviors in toddlers and adults looking at images of faces and blocks, as well as large number of adults looking at movies or static images. The distributional aspects of the number of fixations may suggest a fractal structure to gaze patterns in free scanning and imply that the incompleteness of standard algorithms may be due to the scale-free behaviors of the underlying scanning distributions. We discuss the nature of this hypothesis, its limitations, and offer directions for future work.

Causality, criticality, and reading words: distinct sources of fractal scaling in behavioral sequences

The finding of fractal scaling (FS) in behavioral sequences has raised a debate on whether FS is a pervasive property of the cognitive system or is the result of specific processes. Inferences about the origins of properties in time sequences are causal. That is, as opposed to correlational inferences reflecting instantaneous symmetrical relations, causal inferences concern asymmetric relations lagged in time. Here, I integrate Granger-causality with inferences about FS. Four simulations illustrate that causal analyses can isolate distinct FS sources, whereas correlational techniques cannot. I then analyze three simultaneous sequences of responses from a database of word-naming trials. I find that two, or perhaps three, distinct sources account for the presence of FS in these sequences, but FS is not a general property of the system. This suggests that FS arises due to the properties of a limited number of identifiable psychological and/or neural processes. Finally, I reanalyze a previously published dataset of acoustic frequency spectra using the new tools. The causality/criticality combination introduced here offers a new important perspective in the study of cognition.