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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.