Space filling curves are a class of fractals that are important mathematical descriptions of the appearance and shape of natural objects. There is growing interest in the modelling of such curves to measure pathology in medicine and biology. This work presents a method of modelling fractal curves, such as the boundary of brain white matter, and partitioning such curves in to segments having equ...

A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space. This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families. Two underlying measures are employed: the mean inter-cluster distance ove...

Abstract In this paper, we study area-filling curves, i.e. continuous and injective mappings defined on [0, 1] whose graph has positive measure. Current literature calls them “Osgood curves”, but their invention is due to H. Lebesgue. Stromberg Tseng constructed homogeneous curves offered an elegant example. We show that appropriate variant of Knopp’s construction attains the same homogeneity r...

There exists a never-ending “arms race” between malware analysts and adversarial malicious code developers as malevolent programs evolve countermeasures are developed to detect eradicate them. Malware has become more complex in its intent capabilities over time, which prompted the need for constant improvement detection defence methods. Of particular concern anti-analysis obfuscation techniques...

A key aspect of the parallel partitioners of AMR codes based on meshes consisting of regularly refined patches lies in the choice of a load balancing algorithm. One of the current load balancing methods of choice is to use a space-filling curve. The need to apply load balancing in parallel on possibly hundreds of thousands of processors has led to the development of an algorithm which generates...