Computation of Lebesgue’s Space-Filling Curve

Journal Title: Computer Reviews Journal - Year 2019, Vol 4, Issue 0

Abstract

The means of realizing or approximating the Lebesgue space-filling curve (SFC) with binary arithmetic on a uniformly spaced binary grid are not obvious, one problem being its formulation in terms of ternary representations; that impediment can be overcome via use of a binary-oriented Cantor set.  A second impediment, namely the Devil’s Staircase feature, also created by the role of the Cantor set, can be overcome via the definition of a “working inverse”, thereby providing means of achieving compatibility with such a grid. The results indicate an alternative way to proceed, in realizing an approximation to Lebesgue’s SFC, which circumvents any complication raised by Cantor sets and is compatible with binary and integer arithmetic. Well-known constructions such as the z-curve or Morton order, sometimes considered in association with Lebesgue’s SFC, are treated as irrelevant.

Authors and Affiliations

Arthur R Butz

Keywords

Related Articles

Make Semantic Analysis of Opinions about social networking using Blog Search Engines

There is no consensus amongst the academic communities weather Social media is a boon or bane for the students.  Semantic analysis and blog search was used to get extracts opinions of the bloggers regarding various aspec...

Geographic Information Systems: A Survey

At its core GIS or Geographical Information System, is a mapping tool that allows various types of information to be linked to geolocation. With advances in Big Data technologies, the availability of a large and ever-inc...

An Artificial Human Optimization Algorithm titled Human Thinking Particle Swarm Optimization

Artificial Human Optimization is a latest field proposed in December 2016. Just like artificial Chromosomes are agents for Genetic Algorithms, similarly artificial Humans are agents for Artificial Human Optimization Algo...

The Energy Efficient FIR Filter for Biomedical Application using FPGA

This research work proposes a low power Finite Impulse Response (FIR) digital filter system using Field Programmable Gate Array (FPGA) to filter biomedical signals. A major issue regarding such implementations is associa...

Comparative Analysis of Predictive Models for the Likelihood of Infertility in Women Using Supervised Machine Learning Techniques

Infertility is a worldwide problem, affecting 8% – 15% of the couples in their reproductive age. WHO estimates that there are 60 - 80 million infertile couples worldwide with the highest incidence in some regions of Sub-...

Download PDF file
  • EP ID EP655232
  • DOI -
  • Views 123
  • Downloads 0

How To Cite

Arthur R Butz (2019). Computation of Lebesgue’s Space-Filling Curve. Computer Reviews Journal, 4(0), 1-17. https://europub.co.uk/articles/-A-655232