JOURNAL ARTICLE

3D RENDERING OF THE QUATERNION MANDELBROT SET WITH MEMORY.

  • Published In: Fractals, 2024, v. 32, n. 3. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: FARIELLO, RICARDO; BOURKE, PAUL; ABREU, GABRIEL V. S. 3 of 3

Abstract

In this paper, we explore the quaternion equivalent of the Mandelbrot set equipped with memory and apply various visualization techniques to the resulting 4 -dimensional geometry. Three memory functions have been considered, two that apply a weighted sum to only the previous two terms and one that performs a weighted sum of all previous terms of the series. The visualization includes one or two cutting planes for dimensional reduction to either 3 or 2 dimensions, respectively, as well as employing an intersection with a half space to trim the 3 D solids in order to reveal the interiors. Using various metrics, we quantify the effect of each memory function on the structure of the quaternion Mandelbrot set. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Fractals. 2024/04, Vol. 32, Issue 3, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:0218-348X
  • DOI:10.1142/S0218348X24500610
  • Accession Number:177091116
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