50. 4, 0. 6, 0. 8, 1. 0, 1. 2, 1. 4, 1. 6, 1. 8, 2. 0, and 2. 2) were factorially combined with seven temporal exponents( a50. 2, 0. 4, 0. 6, 0. 8, 1. 0, 1. 2, and 1. 4) to create the 70 dynamic image sequences we employed. The resultingﬁltered spectra were inverse Fourier transformed to gray-scale levels for display. For noise stimuli the traditionalmeasures of contrast have proved inadequate. A usefulmetric of noise contrast is root mean square (RMS)contrast, 25which we express here in percentage terms as the standard deviation of the gray levels in the display di-vided by the mean. The standard deviation and mean ofthe gray-scale distribution in each stimulus were mea-sured. The gray levels in the ﬁnal image were thenrenormalized to a standard deviation of 28 and a meanlevel of 127, corresponding to a RMS contrast of 22%. 4. Procedure Observers were asked to provide a written description of the phenomenal appearance of each fractal sequence andwere free to use any terms they chose. They were givenan unlimited amount of time to respond. Each fractal se-quence was shown in a continuous loop until the observerindicated readiness to proceed to the next display. Thefractals were presented one at a time in order, starting with the lowest spatial and temporal exponents. All tem-poral exponents were shown for a given spatial exponentbefore the spatial exponent was increased. C. Results and Discussion There was considerable regularity across the four observ-ers' descriptions, so the responses were combined to pro-duce a consensus map of the appearance of the spatiotem-poral texture space (see Fig. 2). Very idiosyncratic termsprovided by some of the subjects were replaced by moregeneral terms consistent with that description. As ex-pected from previous work, 5-8,26,27the primary effect of increasing the spatial exponent bwas to increase the ap-parent coarseness of the fractal texture (see Fig. 3 for anillustration of the effect of bon static fractal textures). The primary effect of increasing the temporal exponent a was to decrease the apparent speed and jitter of the dy-namic textures. Perceptually, for aexponents of 0. 2 and 0. 4, the motion appeared very jittery; e. g., motion to theright was more often than not followed by motion to theleft. In the theory of fractional (biased) Brownian mo-tions, such behavior is called antipersistent and is differ-entiated from random (Brownian) motions and persistentmotions. 28-31Interestingly, when the spatial and tempo-ral exponents were both within the range of natural im-ages, the subjects tended to provide real-world descrip-tions of the stimuli. There were strong interactions between the spatial and temporal dimensions for the appearance of dynamic tex-ture. There are three primary examples of this interac-tion. First, the emergent texture regions were oftenmore apparent, larger, and more diffuse at higher tempo-ral exponents (slower speeds). Second, when the tempo-ral exponent was between 0. 6 and 1. 0, the texture oftenappeared to rotate, but only for smaller spatial exponents. Finally, when the temporal exponent was between 0. 4 and0. 8 and the spatial exponent was small, there was a ten-dency to see two transparent textures, with one moving infront of the other. 3. EXPERIMENT 2: DISCRIMINATION OF DYNAMIC TEXTURES A. Introduction In addition to being able to anticipate the appearance of an aperture color, given its CIE coordinates, color re-searchers are also able to gauge how tolerant subjectswould be to small perturbations in the CIE coordinates. Several studies, especially Wright's and Mac Adam's pio-neering work, 32-35have measured the just noticeable dif-ferences for perturbations of CIE coordinates. Becausethe CIE space is usually depicted as a plane, the locus of JNDs around a single point is usually an ellipse. A mapof such ''Mac Adam ellipses'' in the CIE space (Fig. 4) is auseful tool, which we wished to characterize for the spa-tiotemporal random-fractal space. So far as we areaware, prior fractal discrimination studies have been lim-ited to spatial discrimination. 26,27 Fig. 3. Static, random phase, fractal-like textures produced by 1/fbspatial-frequency ﬁltering of random white noise. Static snapshots of ﬁve of the ten fractal exponents (for one seed valueof the random number generator) are shown here. From top tobottom, the values of the exponent bare 0. 4, 0. 8, 1. 2, 1. 6, 2. 0. Note that as the spatial exponent increases, the apparent coarse-ness of the texture also increases. Billock et al. Vol. 18, No. 10/October 2001/J. Opt. Soc. Am. A 2407