Space-filling curves: Their generation and their application to bandwidth reduction

This paper introduces a class of finite-state algorithms which characterize self-similar space-filling curves. The curves enable one to continuously map a line onto an -dimensional cube, and find application in compressing the bandwidth of arbitrary waveforms. The bandwidth compression is effected in return for an increased susceptibility of the signal to perturbations. The algorithms are represented in a diagrammatic form which enables one to convert the coordinates of a point in a cube into a single number representing the distance along a space-filling curve, or vice-versa, merely by visual inspection. The diagrams are always finite in size and may be constructed by following a rather simple numerical procedure.