Writing sequences on the plane

The problem of arranging two-dimensional arrays of data into one-dimensional sequences comes up in image processing, color quantization, and optical and magnetic data recording. A good arrangement should enable the one-dimensional sequences to be modeled as Markov chains or shifts of finite type. Since this is not possible in general, two-dimensional data is most commonly scanned by rows, columns, or diagonals. We look into three unusual ways to write a sequence in the plane: by Penrose tilings, by space-filling curves, and by cylindrical and spiral lattices. We show how Penrose tilings can be used to record information and how some spiral lattices can be used for quantization of color spaces.