Measures of chromatic contrast sensitivity in children are lower than those of adults. This may be related to immaturities in signal processing at or near threshold. We have found that children's VEPs in response to low contrast supra-threshold chromatic stimuli are more intra-individually variable than those recorded from adults. Here, we report on linear and nonlinear analyses of chromatic VEPs recorded from children and adults. Two measures of signal-to-noise ratio are similar between the adults and children, suggesting that relatively high noise is unlikely to account for the poor clarity of negative and positive peak components in the children's VEPs. Nonlinear analysis indicates higher complexity of adults' than children's chromatic VEPs, at levels of chromatic contrast around and well above threshold.

*n*= 11, mean age: 28 years, range 26–33, 5 males, 6 females), 10 to 13 years (

*n*= 9, mean age: 11.3 years, 4 M, 5 F), 7 to <10 years (

*n*= 14, mean age: 8.7 years, 6 M, 8 F), and 4.8 to <7 years (

*n*= 8, mean age: 5.9 years, 6 M, 2 F). The children were divided into these three age ranges (approximately early, middle, and late childhood) so that maturational changes could be investigated. All participants had normal visual acuity, color vision (on screening with Ishihara pseudoisochromatic plate test), no ocular abnormality (as assessed by direct undilated ophthalmoscopy), no amblyopia, or uncorrected astigmatism.

*x*= 0.305,

*y*= 0.310) and luminance (20 cd m

^{−2}). Because of known raster and oblique effects (Rabin, Switkes, Crognale, Schneck, & Adams, 1994), the stimuli were oriented obliquely (45° or 135°) rather than horizontally and vertically. The grating stimuli were centrally located, to avoid isoluminance variations with retinal location (Bilodeau & Faubert, 1999; Kulikowski, Robson, & McKeefry, 1996), presented as a square patch with sides subtending an angle of 5°. At maximum contrast, the colors were of CIE chromaticity coordinates

*x*= 0.38,

*y*= 0.27 (magenta) and

*x*= 0.23,

*y*= 0.35 (cyan), resulting in cone excitations of L

_{magenta}= 12.1, L

_{cyan}= 14.4, M

_{magenta}= 5.6, M

_{cyan}= 7.9, S

_{magenta}= 0.21, S

_{cyan}= 0.20. If cyan is regarded as the stimulus color and magenta as the background color, the L-, M- and S-cone contrasts elicited were −0.16, 0.40, and −0.07 (Cole & Hine, 1992). In the present study, chromatic contrast threshold was expressed as a percentage of maximum available chromatic contrast. The spatial, temporal, and chromatic parameters of the stimuli were chosen to stimulate the L–M chromatic contrast system preferentially (Kulikowski, McKeefry, & Robson, 1997; McKeefry, Russell, Murray, & Kulikowski, 1996; Mullen, 1985; Murray, Parry, Carden, & Kulikowski, 1987; Rabin et al., 1994; Suttle & Harding, 1999) while minimizing the effects of chromatic aberration (Flitcroft, 1989).

_{color1}/ (L

_{color1}+ L

_{color2})) was varied by the participant (method of adjustment). For nine of the adults and three of the children, stimuli were at their individual isoluminance color ratios. The remaining participants were tested at the average isoluminance color ratio of a larger group of adult participants. Two of the adults were tested using an average value as their VEPs because no individual isoluminance measure was made. Most of the children were tested using an average adult value as the concept of minimal flicker in the heterochromatic flicker photometry task was difficult to grasp in preliminary work on children. Previous researchers have used mean adult values for isoluminance as an approximation of the color ratio of children's isoluminance (Crognale, 2002; Till, Westall, Koren, Nulman, & Rovet, 2005) and this has been assessed as a valid procedure under certain conditions (Pereverzeva, Hui-Lin Chien, Palmer, & Teller, 2002) so an average adult value was used with the understanding that luminance cues may be introduced if the participant's individual isoluminance color ratio is different from the average isoluminance color ratio employed.

*y*(

*t*

_{1}),

*y*(

*t*

_{2}),…) were converted into evolving sets of coordinates in different dimensions of phase space using the following formula:

*X*

_{ i}= (

*y*(

*t*

_{ i}),

*y*(

*t*

_{ i}+

*τ*),

*y*(

*t*

_{ i}+ 2

*τ*),…,

*y*(

*t*

_{ i}+ (

*m*− 1)

*τ*), where

*X*

_{ i}is the reconstructed phase space trajectory,

*m*is the embedding dimension,

*τ*is a constant known as the delay time, and the index

*i*denotes ordering in time. In the present study, two delay times (

*τ*= 4 ms and 6 ms) were used and the correlation dimension,

*D*

_{2}, was estimated for five embedding dimensions in phase space,

*m*= 1, 2, 3, 4, and 5.

*r*

_{min}) and the logarithm of the largest distance (represented by

*r*

_{max}) were computed. A series of “bins” was then created to record the Correlation Sum,

*C*(

*r*), which is the normalized number of pairs of points with a separation distance of less than a specified distance

*r*. In this study, 64 bins (an arbitrary number) were used and the width of each bin was set to (

*r*

_{max}−

*r*

_{min}) / 64. Thus, from first to last, the separation distances used in the analysis were defined by the series

*r*

_{1},

*r*

_{2},…

*r*

_{ n}, where the radius

*r*

_{ n}=

*r*

_{min}+

*n*(

*r*

_{max}−

*r*

_{min}) / 64, where

*n*= 1 to 64.

*D*

_{2}is then approximated by

*D*

_{2}∼ log(

*C*(

*r*)) / log(

*r*) (Grassberger and Procaccia, 1983a, 1983b). “∼” indicates that this is a scaling relationship, so

*D*

_{2}was calculated as the slope, dlog(

*C*(

*r*)) / dlog(

*r*), of the linear scaling portion of the plot of log(

*C*(

*r*)) versus log(

*r*). In this study, the slope of the scaling portion of the plot was calculated by determining the slopes of

*i*consecutive local portions of the plots, with each portion consisting of

*k*consecutive points (

*k*= 6, 12), and finding a local maximum slope in a region where the slopes were relatively constant. The slope for each

*i*th portion was determined to be the slope of the line of best fit (least squares method) drawn through the points that were part of the

*i*th portion of the plot.

*D*

_{2}as a function of

*m*for these data (Theiler et al., 1992). The plateau index (PI; Boon et al., 2008) was calculated to determine whether the function plateaued. PI < 0.3, where PI = (

*D*

_{2}at

*m*= 5) − (

*D*

_{2}at

*m*= 4) was taken to indicate that the function did plateau. PI was compared between VEP and surrogate data to determine whether the VEPs were nonlinear.

*W*was used.

*p*= 0.39), no significant interaction between type of SNR and age group (

*p*= 0.63), and no significant interaction between stimulus contrast and age group (

*p*= 0.61). Pairwise comparisons indicated that the SNR of 42% was significantly different from all other chromatic contrasts (

*p*< 0.0001, Bonferroni corrected) but that SNR of 2T%, T%, and 0% were not significantly different from each other (

*p*ranged from 0.08 to 1.00, Bonferroni corrected). Pairwise comparisons also indicated that SNR2 was lower than SNR1 estimates (

*p*< 0.0001, Bonferroni corrected) by approximately 0.38.

*D*

_{2}) of all of the VEP data combined (responses to all contrast levels) and their surrogates for each age group are presented in Figure 4. The plateau index was also determined and compared across VEP and surrogate data, as shown in Figure 5. The surrogate and VEP measures were found to be significantly different (

*p*< 0.05) indicating that the

*D*

_{2}of the VEPs recorded from children is the fractal dimension of a nonlinear dynamical system, which is not equivalent to stochastic noise. Therefore, the correlation dimension at

*m*= 5 may be considered an estimate of the fractal dimension of the underlying system.

*F*(3, 33) = 33.141,

*p*< 0.0001). There was no interaction between stimulus contrast and age group (

*F*(9, 105) = 0.942,

*p*= 0.492). There was a significant within-subjects effect of stimulus contrast (

*F*(3, 105) = 40.074,

*p*< 0.0001) and a significant effect due to age group (

*F*(3, 35) = 14.374,

*p*< 0.0001). Paired comparisons indicated that the fractal dimensions of the adult VEPs were significantly different from each of the child groups (

*p*< 0.0001), but that the children's groups were not significantly different from each other (

*p*= 0.68 to 0.94). The children's fractal dimension data were lower than the adult data by an average of 0.55 ( Figure 6). Paired comparisons also revealed that the fractal dimension for all chromatic contrasts were significantly different from each other (

*p*≤ 0.002) except for 2T% and 0% (

*p*= 0.419). Thus, the order from lowest to highest fractal dimension VEP was 42%, 2T% = 0%, T%. This trend is similar in children and adults (see also Boon et al., 2008).

*R*= −0.56,

*p*= 0.005,

*n*= 24; 7 to <10 years old,

*R*= −0.38,

*p*= 0.03,

*n*= 32; 10 to 13 years old,

*R*= −0.49,

*p*= 0.006,

*n*= 30), which was also true for the adults' data (see also Boon et al., 2008). Pearson's correlation also showed that fractal dimension and power are moderately negatively correlated for VEPs in response to stimulus contrasts above zero (42%, 2T%, T%; 4.5 to <7 years old:

*R*= −0.62,

*p*= 0.002;

*n*= 24; 7 to <10 years old,

*R*= −0.55,

*p*= 0.002,

*n*= 29; 10 to 13 years old,

*R*= −0.67,

*p*< 0.0001,

*n*= 28).

*W*(coefficient of concordance) was calculated. For each age group, the highest fractal dimension was attributable to T% chromatic contrast, followed by 2T% and 42%. However, the degree of concordance of rankings within each group differed between age groups. It was strongest in the adults (Kendall's

*W*= 0.83,

*p*= 0.001; data from Boon et al., 2008), then the youngest children (Kendall's

*W*= 0.67,

*p*= 0.005), the second youngest group of children (Kendall's

*W*= 0.49,

*p*= 0.007) and lowest in the oldest group of children (Kendall's

*W*= 0.48,

*p*= 0.008). As shown by Figure 7 (center column), correlation dimension was more strongly correlated with power in children than in adults (Spearman's rho = 0.30,

*p*= 0.09; data from Boon et al., 2008). The degree of concordance of rankings was moderate in the youngest age group (Kendall's

*W*= 0.67,

*p*= 0.004) and middle age group of children (Kendall's

*W*= 0.49,

*p*= 0.007) and low in the oldest group of children (Kendall's

*W*= 0.37,

*p*= 0.02).

*F*(3, 33) = 24.911,

*p*< 0.0001, ANOVA; mean difference: 17.1–19.6 years older;

*p*≤ 0.03), but the other groups were not significantly different from each other. When morphology category was examined for differences in fractal dimension, again the N-EP morphology group was found to be significantly different from each of the other groups (

*F*(3,29) = 6.757,

*p*= 0.001, ANOVA; mean difference: 0.10 to 0.15 higher in fractal dimension than other groups;

*p*≤ 0.047), but the other groups were not significantly different from each other.

*m*= 5. Therefore, the correlation dimension at

*m*= 5 may be regarded as an estimate of the fractal dimension of the dynamical system. Of the stimuli modulated in chromatic contrast (42%, 2T%, and T%), T% had the highest mean fractal dimension in all age groups. This finding could be taken to suggest that the fractal dimension may prove useful as a preliminary discriminant of chromatic contrast threshold in both adults (Boon et al., 2008) and children. In addition, the fractal dimension was significantly different between 42%, 2T% and T% and 0% in both children and adults (grouped data) despite the VEP morphology between 2T%, T% and 0% being indistinguishable in the children. As the Kendall

*W*results showed, the fractal dimension was not a strong indicator of psychophysical threshold for individual child participants, indicating that it is not likely to be generally useful as an indicator of contrast threshold in children. Subtle differences in 42% VEP morphology between children in the three age groups were not reflected in the fractal dimension, which was similar across the three age groups. However, this may be because the group averaged VEP morphologies do not fully reflect the variability of the morphology of individuals within each of the children's age groups. In each age group, there were individuals with and without late components, with and without early N-peaks and shoulders ( Figure 8). Instead, the fractal dimension appeared to be associated with the most obvious difference between the adult and child VEPs, which was the order and magnitude of the largest repeatable VEP components (PN in the children and NP in the adults).