Fractal Analysis

Brown, Clifford T.; Liebovitch, Larry S.

doi:10.4135/9781412993876

Cited by 57 publications

(27 citation statements)

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“…Especially for the two fastest paces, the power spectrum almost seemed to exhibit multiscaled fractal properties (Brown & Liebovitch, 2010) as the low frequencies appeared to obey a much shallower scaling relation compared with the faster frequencies. This may reflect the limited size of the nine-dot display, which effectively acts as an environmental constraint on the variance of the eye movement fluctuations (Van Orden, Hollis, & Wallot, 2012).…”

Section: Discussionmentioning

confidence: 96%

Interdependence of Saccadic and Fixational Fluctuations

Wallot

Coey

Richardson

2015

Ecological Psychology

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Recent research suggests that the different components of eye movements (fixations, saccades) are not strictly separate but are interdependent processes. This argument rests on observations that gaze-step sizes yield unimodal distributions and exhibit power-law scaling, indicative of interdependent processes coordinated across timescales. The studies that produced these findings, however, employed complex tasks (visual search, scene perception). Thus, the question is whether the observed interdependence is a fundamental property of eye movements or emerges in the interplay between cognitive processes and complex visual stimuli. In this study, we used a simple eye movement task where participants moved their eyes in a prescribed sequence at several different paces. We outlined diverging predictions for this task for independence versus interdependence of fixational and saccadic fluctuations and tested these predictions by assessing the spectral properties of eye movements. We found no clear peak in the power spectrum attributable exclusively to saccadic fluctuations. Furthermore, changing the pace of the eye movement sequence yielded a global shift in scaling relations evident in the power spectrum, not just a localized shift for saccadic fluctuations. These results support the conclusion that fixations and saccades are interdependent processes.

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Section: Discussionmentioning

confidence: 96%

Interdependence of Saccadic and Fixational Fluctuations

Wallot

Coey

Richardson

2015

Ecological Psychology

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“…e more general outcome appears to be nonstationary α values that uctuate within the course of a task performance (Ihlen & Vereijken, 2010). Multifractal analysis addresses this question of the quantity and the heterogeneity of α values that describe a data series (Brown & Liebovitch, 2010).…”

Section: Multifractal Analysismentioning

confidence: 99%

Fractal and recurrence analysis of psycholinguistic data

Wallot

O’Brien

Orden³

2012

Benjamins Current Topics

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is chapter illustrates nonlinear methods of data analyses for timeseries of reading times, obtained from a self-paced reading task. We present reading data obtained from adult readers, highlighting di erences in reading uency between literate adults (Wallot & Van Orden, 2011b, c), as well as reading data obtained from 2nd, 4th, and 6th graders, highlighting di erences in reading performance between children of di erent ages. ese two di erent data sets illustrate choices that are encountered when nonlinear analysis techniques of timeseries are employed, and we will discuss solutions to maximize the validity and reliability of the analyses.Study 1 concerns the adult data which present a three-factor design with two levels of each factor (i.e., 2 x 2 x 2): the size of the text unit -word units versus sentence units; the uency of readers -Ph.D. candidates in English literature versus undergraduates from an introduction to psychology course; and text repetition -rst reading versus a subsequent reading. e nonlinear methods illustrated are timeseries analyses, which give information about the hypothetical system dynamics that could have produced the time-ordered variability observed across reading times. e payo from these analyses is new information about performance over-and-above and di erent from the results of conventional analyses.Study 2 concerns the children's reading data containing only a single factor, grade level (2nd, 4th, and 6th). Nonlinear methods here illustrate the di erences between the reading performance of the older and younger children, to describe the acquisition of reading skill.In both cases, conventional analyses reveal little about the systems under study. e nonlinear analyses, on the other hand, reveal di erences due to the text unit conditions and the reading uency of the adult's performance, as well as di erences in reading performance across the groups of children. e results give

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“…22 This dynamical process creates fractals, which are objects whose smallest particles have the same structure as the composite whole of these particles. 23 As the building blocks of humans and human groups are essentially cooperating single cells (10% body cells and 90% microbes), they might behave in a similar way. My theory is that at each level of cooperation (organ, organism, group, state, global society) their behaviour will be steered by the biological requirements of feeding, growth, reproduction, multiplication, spreading, stability and reciprocity.…”

Section: Biological Foundations Of Lawmentioning

confidence: 99%

Integrating the Disciplines of Law and Biology: Dealing with Clashing Paradigms

Gommer

2015

ULR

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Fractal Analysis

Cited by 57 publications

References 0 publications

Interdependence of Saccadic and Fixational Fluctuations

Interdependence of Saccadic and Fixational Fluctuations

Fractal and recurrence analysis of psycholinguistic data

Integrating the Disciplines of Law and Biology: Dealing with Clashing Paradigms

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