The existence condition of grid filling curves

摘要

In a grid space, a curve which spans all grid points is called a grid fillin9 curve. A number of grid filling curves have been proposed and studied. Hubert curves and Peano curves are examples of popular grid filling curves. However, they are defined only when some sever size constraints. In this paper, we show the necessary and sufficient condition for the existence of grid filling curves and their constructions.