Abstract
This chapter discusses an algorithm for Peano curve generation. The Peano curve is a fractal with integer-fractal dimension. This curve provides a continuous mapping from the integers to n-space, with the properties that all points in the domain are close in the range, and most points that are close in the range are close in the domain. Applications found include image compression, color quantization, and debugging for interactive four-dimensional rotation routines. The Butz's algorithm (1971) is implemented for generating an n-dimensional Peano curve to m bits of precision, that is, with 2m segments per dimension, 2mn segments total. It is based on bitwise Boolean operations. But the code's correct operation has been verified in two, three, and four dimensions. The chapter gives an example in two dimensions. The algorithm, but not its derivation, is described by Butz (1971).
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