We present a fractal technique for addressing geometric analogy problems from the Raven's Standard Progressive Matrices test of general intelligence. In this method, an image is represented fractally, capturing its inherent self-similarity. We apply these fractal representations to problems from the Raven's test, and show how these representations afford a new method for solving complex geometric analogy problems. We present results using the fractal algorithm on all 60 problems from the Standard Progressive Matrices version of the Raven's test.
In the past, many knowledge representation systems failed because they were too monolithic and didn't scale well, whereas other systems failed to have an impact because they were small and isolated. Along with this trade-off in size, there is also a constant tension between the cost involved in building a larger community that can interoperate through common terms and the cost of the lack of interoperability. Its main contribution is in recognizing and supporting the fractal patterns of scalable web systems. In this article we discuss why fractal patterns are an appropriate model for web systems and how semantic web technologies can be used to design scalable and interoperable systems.
Fitzgerald, Tesca (Georgia Institute of Technology) | McGreggor, Keith (Georgia Institute of Technology) | Akgun, Baris (Georgia Institute of Technology) | Goel, Ashok K. (Georgia Institute of Technology) | Thomaz, Andrea L. (Georgia Institute of Technology)
Learning by observation is an important goal in developing complete intelligent robots that learn interactively. We present a visual analogy approach toward an integrated, intelligent system capable of learning skills from observation. In particular, we focus on the task of retrieving a previously acquired case similar to a new, observed skill. We describe three approaches to case retrieval: feature matching, feature transformation, and fractal analogy. SIFT features and fractal encoding were used to represent the visual state prior to the skill demonstration, the final state after the skill has been executed, and the visual transformation between the two states. We discovered that the three methods (feature matching, feature transformation, and fractal analogy) are useful for retrieval of similar skill cases under different conditions pertaining to the observed skills.
Alex P. Pentland Artificial Intelligence Center, SRI International 333 Ravenswood Ave., Menlo Park, California 94025 ABSTRACT Shape-from-shading and shape-from-texture methods have the To accomplish this, we must have rccour8e to a 3-D model competent to describe both crumpled surface8 and smooth ones. The fractal model of surface shape [6,7] appears to possess the required properties. Evidence for this comes from recently conducted surveys of natural imagery [6,8]. These survey found that the fractal model of imaged 3-D surfaces furnishes an accurate description of most textured and shaded image regions. Perhaps even more convincing, however, is the fact that fractals look like natural surfaces [9,10,11].
In one way, Jackson Pollock's mathematics was ahead of its time. When the reclusive artist poured paint from cans onto vast canvases laid out across the floor of his barn in the late 1940s and early 1950s, he created splatters of paint that seemed completely random. Some interpretations saw them as a statement about the futility of World War II, others as a commentary on art as experience rather than representation. As Pollock refined his technique over the years, critics became increasingly receptive to his work, launching him into the public eye. "We have a deliberate disorder of hypothetical hidden orders," one critic wrote, "or'multiple labyrinths.' " In 1999, Richard Taylor, a physicist at the University of Oregon, expressed the "hidden orders" of Pollock's work in a very different way.