Within each type of discrimination, the order of presenta-tion of the fractal exponents was randomized, with eachobserver receiving a different random order. We alsorandomized the ''seed'' values of the random number gen-erator used to generate the white noise before ﬁltering. The same seed values were used within each staircase butnot for subsequent staircases. Thus the data in Figs. 5-9, which are collapsed across subjects or conditions, represent discrimination for an ensemble of randomphase spectra rather than any particular pattern of ran-dom phases. Each subject required roughly 50 h to com-plete the measurements. C. Results and Analysis Figure 5 plots just-noticeable-difference contours (analo-gous to Mac Adam ellipses) for the dynamic fractals. It isinteresting to note that the ellipse size is fairly constantover much of the space. In color, much attention hasbeen devoted to obtaining colorimetric spaces in whichdiscrimination thresholds are relatively constant: the socalled Uniform Color Spaces (e. g., CIE 1976 Uniform Color Space). 1,2The spatial and temporal discrimina-tions will be discussed separately in more detail below. 1. Spatial Just-Noticeable Differences Overall, spatial discriminations were easiest when bwas between 1. 4 and 1. 8. This is consistent with previous re-search on static fractal discrimination. 26,27Spatial JND's are plotted in Fig. 6 as a function of spatial expo-nent. The data for both Above and Below JND's are re-markably similar across subjects. 2. Effect of Temporal Characteristics on Spatial Discriminations If the spatial and temporal dimensions are independent in dynamic fractals, as is often assumed, similar discrimi-nation thresholds should be found for dynamic fractals re-gardless of temporal exponent. Figure 7 helps to illus-trate the point that the spatial JND's did not vary muchas a function of the temporal nature of the stimuli. Al-though there is a slight suggestion of lower spatial JNDsfor the lowest temporal exponents, it seems that spatialdiscriminations are largely independent of the temporalcharacteristics in the stimuli. 3. Temporal Just-Noticeable Differences Figure 8 plots the temporal JND's as a function of tempo-ral exponent. For each subject, temporal discriminationswere easiest when awas between 0. 8 and 1. 0, a typical range of exponents for natural stimuli. 15-18The pattern of discriminations was remarkably consistent across sub-jects. Of particular interest is that the antipersistentstimuli were extremely difﬁcult to discriminate. More-over, for three of the four subjects, the Below JND's forthe antipersistent stimuli tended to be elevated forsmaller temporal exponents. Notice that for these three Fig. 5. Wright-Mac Adam-like contours for discrimination thresholds in four directions in a spatiotemporal fractal space. Average of four observers. The contours are simple quarter-circles ﬁtted to the JNDs that span their quadrants. These contours are not theo-retically motivated and are used to reduce the confusion that occurs for overlapping JND crosses. Note that over a wide range of thespace the discrimination thresholds vary only slightly; e. g., the space approaches the ideal of a uniform colorimetric space (such as the CIE 1976 uniform chromaticity space). 1,2Billock et al. Vol. 18, No. 10/October 2001/J. Opt. Soc. Am. A 2409