Analysis of 4D Hypercomplex Generalizations of Julia Sets

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• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9972
• 期：1
• 页码：627-635
• 全文大小：5,748 KB
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• 作者单位：Andrzej Katunin (17)
  
  17. Institute of Fundamentals of Machinery Design, Silesian University of Technology, 18A Konarskiego Street, 44-100, Gliwice, Poland
  
• 丛书名：Computer Vision and Graphics
• ISBN：978-3-319-46418-3
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9972

文摘

All possible 4D hypercomplex vector spaces were considered in the light of an ability of construction of Julia fractals in them. Both arithmetic fundamentals of the considered algebras as well as implementation procedures of such hypercomplex numbers are given. In the paper, the presented study summarizes well-known 4D hypecomplex fractals, like bicomplex and quaternionic ones, introduces a group of new hypercomplex fractals, like biquaternionic, and shows why other 4D hypercomplex vector spaces cannot produce the non-trivial Julia sets. All of the considered cases were enriched by several graphical representations of hypercomplex Julia sets with their graphical analysis.