Space-filling curves map the multi-dimensional space into the one-dimensional space. A space-filling curve acts like a thread that passes through every cell element (or pixel) in the n-dimensional space so that every cell is visited only once, i.e., the space-filling curve does not self-intersect. Thus, a space-filling curve imposes a linear order of the cells in the n-dimensional space. This i...

Several space-filling and related curves are described by means of ”simultaneous grammars”. From these descriptions it is very easy to obtain short procedures in logo for drawing the curves.

Space-filling curves have been widely used in mathematics and to transform multi-dimensional problems into one-dimensional forms. For scientific applications, ordering data or computation along spacefilling curves can be useful for exploiting locality when partitioning onto parallel systems or when restructuring to exploit memory hierarchy. In this paper, we present an efficient approach for en...

Space-filling curves (SFC, also known as FASS-curves) are a useful tool in scientific computing and other areas of computer science to sequentialize multidimensional grids in a cache-efficient and parallelization-friendly way for storage in an array. Many algorithms, for example grid-based numerical PDE solvers, have to access all neighbor cells of each grid cell during a grid traversal. While ...

In this note, we construct curves over finite fields which have, in a certain sense, a “lot” of points, and give some applications to the zeta functions of curves and abelian varieties over finite fields. In fact, we found the basic construction, given in Lemma 1, of curves in A which go through every rational point, as part of an unsuccessful attempt to find curves of growing genus over a fixe...

We consider the use of space-filling curves (SFC) in scanning control parameters for quantum chemical systems. First we show that a formally exact SFC must be singular in the control parameters, but a finite discrete generalization can be used with no problem. We then make general observations about the relevance of SFCs in preference to linear scans of the parameters. Finally we present a simp...