A theory of general intelligence must account for how an intelligent agent can map percepts into actions at the level of human performance. We sketch the outline of a new approach to this perception-to-action mapping. Our approach is based on four ideas: the world exhibits fractal self-similarity at multiple scales, the structure of representations reflects the structure 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 three parts. In the first part, we describe the nature of visual analogies and fractal representations. In the second, we illustrate a technique of fractal analogies and show how it gives human-level performance on an intelligence test called the Odd One Out. In the third, we describe how the fractal technique enables the percept-to-action mapping in a simple, simulated world.