In this paper we describe how the art of weaving can be applied to fiber optics in order to produce precisely controlled reproducible image guides and image dissectors. As examples of the types of device for which woven fiber optics are applicable, we describe a 3:1 interleaver for use with a cathode-ray tube to produce color images, and a high speed alpha numeric output device. The techniques of weaving fiber optics are discussed in sufficient detail in order to allow for further work. Although, in principle, one might be able to weave glass optical fibers, all the work described here made use of plastic optical fibers 0.25 mm in diameter.