Fractals are geometric objects of inexhaustible detail. Fractal structures have been found in the contours of mountain ranges, the patterns of veins on a leaf, and the fluctuations of the Dow Jones Industrial Average. The endeavor of inventing new technologies, consisting of a hierarchical network of practical inquiries, exhibits fractal properties as well. Among these are multiplicity, latency, and self-similarity. Multiplicity means that a single inventive idea may lead to an immense and diverse array of technological artifacts. Latency means that the potential of an inventive idea to yield practical embodiments only reveals itself in time, and may never be fully known. Self-similarity means that invention is not scale-dependent; in other words, breakthroughs and refinements may be difficult, in principle, to distinguish. Invention, as a whole, resembles an ever-expanding fractal island of promontory upon promontory. Patent law assigns a particular inventor legal rights to a portion of that intricate coastline. The fractal properties of multiplicity, latency, and self-similarity contribute to many of the perennial difficulties in patent law, including fixing the meaning of claim language, properly applying the enablement and written description requirements, and identifying “abstract ideas” that cannot be patented. Understanding the fractal properties of invention is an important step in addressing these issues.