Fractals are patterns that show self-similarity at different levels of scale. Typically they appear in nature and this degree of similarity is approximate or statistical. However, artificial or exact fractals have also been studied and the advantage of these stimuli is the ability to more carefully control the relationships that occur across various hierarchies. In two experiments we studied the perceived beauty of a novel class of exact visual fractal in which we introduced reflection, rotation, translation, and random symmetries that repeated at a local and global levels. Rotation and reflection were consistently preferred to translation and randomness. Only reflected patterns were preferred at a vertical orientation. For all other symmetries there was no difference in preference between vertical and horizontal. In a second experiment we progressively eliminated the salience of local symmetry through opaque shading . Perceived beauty decreased with an increase in shading . For these patterns greater discriminability of their fractal quality makes them more aesthetically appealing.
Measurement of formation resistivity through casing is an emerging logging technology, with prototype logging tools currently under development. Modeling studies show that the presence of cement could reduce the sensitivity of the TCRT [TM] (Through Casing Resistivity Tool [TM]). Physically this tool has some similarity to a laterolog. Measurements would be seriously affected if the cement was much more resistive than the formation. We have carried out a laboratory study of cement resistivity with the funding from the Gas Research Institute. Our main objective was to provide hard data to use in assessing the impact of cement resistivity on measurements made with the TCRT [TM]. Our results show that cement resistivity is generally low, varying from less than 1 to 8 -m at 120 degrees F. Light-weight cements were generally the least resistive, with Class A, G and H cements more resistive. Resistivity was essentially independent of either confining or pore pressure. It was also independent of either current density or voltage. Cement resistivity appears to vary with temperature according to Arp's equation, as would be expected for nonconductive material saturated with water. Thin sections and mercury injection capillary pressure data show that porosity in cement is dominantly microporosity, with pore throat diameter less than 0.1 microns. In addition helium porosity is high, ranging from 35 to 40%. The low observed resistivity is due to large amounts of water-filled microporosity. The results of this study signify that the presence of cement will not seriously degrade measurements of resistivity through casing in many environments. Our work concentrated on cements normally used on the North Slope of Alaska, as well as Class H cement, a common Gulf Coast cement. Potential applications of the TCRT [TM] include water flood monitoring at Prudhoe Bay and elsewhere, and detection of "missed pay" behind casing. Introduction Recent technological advances indicate the feasibility of measurement of formation resistivity through casing. Patents on the basic technology are held by Gard et al, Kaufman, and Vail. The concept has been demonstrated by successful measurement of formation resistivity in a cased well. Vail is currently developing a prototype logging tool. The basic concepts for the measurement are described by Kaufman. Early in the development of the technology it was recognized that a high resistivity cement annulus or high casing contact resistance could affect the measurement of formation resistivity. The tool proposed by Vail operates similarly to a laterolog, and is therefore sensitive to the presence of large resistances between the casing and the formation. P. 365^
Frieze patterns appear frequently in architectural designs and ornamental patterning but their aesthetic qualities have never been studied experimentally. In the first experiment, 39 undergraduates used a seven-point rating scale to assess the perceived beauty of the seven basic frieze types presented at a horizontal orientation. The friezes consisted of individual curved and linear motifs as well as random textures. Friezes that filled the entire pattern region and which contained emergent global features were preferred the most. In a second experiment, we utilized horizontal texture friezes that were completely filled and which varied in size and number of elements. Participants preferred patterns with larger features, probably because they make detection of the symmetric transformations more visible. The frieze with the greatest number of symmetries was preferred most but symmetric complexity by itself could not completely account for the predicted preference ordering. In both studies, friezes containing horizontal mirrors (translation, 180° rotation, horizontal mirror, vertical mirror, and glide reflection and translation, horizontal mirror, and glide reflection) were preferred far more than any other condition. Horizontal symmetry may enhance perceived beauty in these cases because it runs parallel to and so emphasizes the overall frieze orientation.
We examine the aesthetic characteristics of row tile patterns defined by repeating strips of polygons. In experiment 1 participants rated the perceived beauty of equilateral triangle, square and rectangular tilings presented at vertical and horizontal orientations. The tiles were shifted by one-fourth increments of a complete row cycle. Shifts that preserved global symmetry were liked the most. Local symmetry by itself did not predict ratings but tilings with a greater number of emergent features did. In a second experiment we presented row tiles using all types of three- and four-sided geometric figures: acute, obtuse, isosceles and right triangles, kites, parallelograms, a rhombus, trapezoid, and trapezium. Once again, local polygon symmetry did not predict responding but measures of correspondence between local and global levels did. In particular, number of aligned polygon symmetry axes and number of aligned polygon sides were significantly and positively correlated with beauty ratings. Preference was greater for more integrated tilings, possibly because they encourage the formation of gestalts and exploration within and across levels of spatial scale.
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