Aztec curve: proposal for a new space-filling curve

TL;DR

This paper introduces the Aztec curve, a new space-filling curve similar to Hilbert's, capable of creating bi-dimensional clusters and demonstrated as effective in compressed sensing applications.

Contribution

The paper proposes the Aztec curve, a novel space-filling curve with unique clustering capabilities and comparable performance to Hilbert in compressed sensing tasks.

Findings

Aztec curve enables bi-dimensional clustering not possible with Hilbert or Peano curves.

In compressed sensing, Aztec curve performs similarly to Hilbert curve.

Aztec curve is a viable new alternative for applications using space-filling curves.

Abstract

Different space-filling curves (SFCs) are briefly reviewed in this paper, and a new one is proposed. A century has passed between the inception of this kind of curves, since then they have been found useful in computer science, particularly in data storage and indexing due to their clustering properties, being Hilbert curve the most well-known member of the family of fractals. The proposed Aztec curve, with similar characteristics to the Hilbert's curve, is introduced in this paper, accompanied by a grammatical description for its construction. It yields the possibility of creating bi-dimensional clusters, not available for Hilbert nor Peano curves. Additional to this, a case of application on the scope of Compressed Sensing is implemented, in which the use of Hilbert curve is contrasted with Aztec curve, having a similar performance, and positioning the Aztec curve as viable and a new alternative for future exploitation on applications that make use of SFC's.