The Adaptive Range of 1/f Isometric Force Production Jacob J. Sosnoff University of Illinois at Urbana-Champaign Andrew D. Valantine and Karl M. Newell Pennsylvania State University The adaptive range of 1/f dynamics in isometric force output was investigated. Participants produced isometric force to targets with predictable demands (constant and sinusoidal) and 1/f noise waveforms (white, pink, brown, and black) that also varied in the frequency bandwidth represented in the force signal (0 – 4 Hz, 0 – 8 Hz, and 0 –12 Hz). The range of within-trial 1/f force dynamics produced was between darker than pink noise and lighter than black noise according to task conditions. The exponent of the respective 1/f force dynamics decreased as the frequency bandwidth of the force signal increased. The findings reveal an adaptive though restricted range of 1/f force variation that is modulated by the dynamics of the task constraints. Keywords: motor control, fractals, isometric force There is growing evidence from a variety of human performance protocols that intra-individual variability, whether calculated on a within- or between-trials basis, is reflective of a 1/f process (Bassingthwaighte, Liebovitch, & West, 1994; Ward, 2002; West, 2006). Voss and Clark (1975) originally demonstrated that the loudness fluctuations in music and speech together with pitch (melody) fluctuations in music exhibit 1/f power spectra. The power spectra of painting and cartoons have also been distin- guished in terms of 1/f properties, and fractal analysis has been used to assess the authenticity of paintings (Taylor, Micolich, & Jonas, 1999). In the variability of standard cognitive and motor laboratory tasks, 1/f properties have been shown for timing and spatial perception (Gilden, Thornton, & Mallon, 1995), reaction time (Clayton & Frey, 1997; Gilden, 1997, 2001; Van Orden, Holden, & Turvey, 2003), standing posture (Duarte & Zatsiorsky, 2000), and isometric force control (Deutsch & Newell, 2003; Sosnoff & Newell, 2005). In spite of the growing evidence for 1/f processes in human performance, it is the case that most demonstrations of 1/f fluctu- ations in properties of the behavioral output do not have 1/f fluctuations specified in the task goal. A primary example of this category of behavior is the 1/f dynamics of reaction time found in the trial-to-trial variability of cognitive tasks (Gilden et al., 1995; Van Orden et al., 2003). As a consequence, evidence of the adaptive range with which individuals can intentionally produce motor output with specific 1/f properties is limited to the indirect demonstrations in artistic performance (Taylor et al., 1999; Voss & Clark, 1975). The main analytical technique utilized to examine 1/f processes in behavioral output is power spectral analysis (Bassingthwaighte et al., 1994). This technique decomposes a time series and reveals the contribution of representative frequency components. Conceptually, each process contributing to the behavior has a unique frequency, and the relative contribution of the process to the behavior is denoted by the amount of power at its characteristic frequency. For instance, if human tracking performance results from two intermittent feedback operators, a dominant visual feedback process operating at 2 Hz and a proprioceptive feedback operator operating at 0.5 Hz (cf. Craik, 1947), spectral analysis would reveal these processes with a large peak at 2 Hz and a smaller peak at 0.5 Hz. However, human motor output does not result from a combination of a few feedback loops but rather from a multitude of interacting feedback and feedforward processes operating at multiple time scales up to approximately 12 Hz (Desmurget & Grafton, 2000; Pew, 1974; Sosnoff & Newell, 2005). The log–log plot of the power spectrum (i.e., log power vs. log frequency) provides an index of how the power (P) changes as a function of frequency (spectral slope, ) and informs about the interaction (i.e., correlation) of underlying processes (Bassing- thwaighte et al., 1994). It is characterized with the equation P(f) = 1/f  . For instance, if there is no change in power as a function of frequency and the spectral slope is 0, then there is no interaction between processes. This is referred to as white noise. In contrast, if the spectral slope is relatively steeper, an exponent of -2 (brown noise) or -3 (black noise), the variations in the behavioral output are due to a few dominant processes, with other processes provid- ing relatively smaller contributions to the output. Pink noise has a spectral slope of -1 and is characterized as a mixture of interac- tion and noninteraction between processes. In isometric force production we have shown that the attempt to produce a constant level of force output leads to multiple time scales of force output (scaling range from 0 to about 10 –12 Hz) that are approximated by a 1/f process (Deutsch & Newell, 2003; Sosnoff & Newell, 2005). The slope of this 1/f scaling regime is dependent on force level, changes with developmental age in young children (Deutsch & Newell, 2003), and the processes of Jacob J. Sosnoff, Department of Kinesiology and Community Health, University of Illinois at Urbana-Champaign; Andrew D. Valantine and Karl M. Newell, Department of Kinesiology, Pennsylvania State Univer- sity. The study was supported in part by National Institute on Aging Grant 1 R03 AG023259. Jacob J. Sosnoff was supported by a Kligman Research Fellowship. Correspondence concerning this article should be addressed to Jacob J. Sosnoff, University of Illinois at Urbana-Champaign, Department of Kinesiology and Community Health, 906 South Goodwin Avenue, 207 Freer Hall, Urbana, IL 61801. E-mail: jsosnoff@uiuc.edu Journal of Experimental Psychology: © 2009 American Psychological Association Human Perception and Performance 2009, Vol. 35, No. 2, 439 – 446 0096-1523/09/$12.00 DOI: 10.1037/a0012731 439 This document is copyrighted by the American Psychological Association or one of its allied publishers. This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.