A theory of general intelligence must account for how an intelligent agent can map percepts into actions at the level of human performance. We describe a new approach to this percept-to-action mapping. Our approach is based on four ideas: the world exhibits fractal self-similarity at multiple scales, the design of mind reflects the design of the world, similarity and analogy form the core of intelligence, and fractal representations provide a powerful technique for perceptual similarity and analogy. We divide our argument into two parts. In the first part, we describe a technique of fractal analogies and show how it gives human-level performance on an intelligence test called the Odd One Out. In the second, we describe how the fractal technique enables the percept-to-action mapping in a simple, simulated world.