A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach
This paper presents a novel technique for visualizing quaternion Julia and Mandelbrot sets of a quaternion-valued polynomial mapping T(q)=qn+mq+c, where q is a quaternion variable, n∈N∖{1}, and m,c are quaternion parameters, by employing the viscosity approximation method. The investigation begins w...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-03-01
|
| Series: | Results in Control and Optimization |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666720725000116 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832582115288416256 |
|---|---|
| author | Nabaraj Adhikari Wutiphol Sintunavarat |
| author_facet | Nabaraj Adhikari Wutiphol Sintunavarat |
| author_sort | Nabaraj Adhikari |
| collection | DOAJ |
| description | This paper presents a novel technique for visualizing quaternion Julia and Mandelbrot sets of a quaternion-valued polynomial mapping T(q)=qn+mq+c, where q is a quaternion variable, n∈N∖{1}, and m,c are quaternion parameters, by employing the viscosity approximation method. The investigation begins with a study of a new escape criterion, specifically designed for generating quaternion Julia and Mandelbrot sets using the viscosity approximation technique. Based on this result, two dimensions and three dimensions cross-sections of quaternion Julia and Mandelbrot sets are created. The paper also examines how variations in the parameters of the iterative methods impact the resulting sets’ characteristics, such as shape, size, symmetry, and color. |
| format | Article |
| id | doaj-art-aaaf2f20edaf4a7381bfc0ca1da7d91c |
| institution | Kabale University |
| issn | 2666-7207 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Control and Optimization |
| spelling | doaj-art-aaaf2f20edaf4a7381bfc0ca1da7d91c2025-01-30T05:15:02ZengElsevierResults in Control and Optimization2666-72072025-03-0118100525A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approachNabaraj Adhikari0Wutiphol Sintunavarat1Department of Mathematics and Statistics, Faculty of Science and Technology Thammasat University, Pathum Thani, 12120, ThailandCorresponding author.; Department of Mathematics and Statistics, Faculty of Science and Technology Thammasat University, Pathum Thani, 12120, ThailandThis paper presents a novel technique for visualizing quaternion Julia and Mandelbrot sets of a quaternion-valued polynomial mapping T(q)=qn+mq+c, where q is a quaternion variable, n∈N∖{1}, and m,c are quaternion parameters, by employing the viscosity approximation method. The investigation begins with a study of a new escape criterion, specifically designed for generating quaternion Julia and Mandelbrot sets using the viscosity approximation technique. Based on this result, two dimensions and three dimensions cross-sections of quaternion Julia and Mandelbrot sets are created. The paper also examines how variations in the parameters of the iterative methods impact the resulting sets’ characteristics, such as shape, size, symmetry, and color.http://www.sciencedirect.com/science/article/pii/S2666720725000116Quaternion Julia setsQuaternion Mandelbrot setsViscosity approximation methodEscaping criterion |
| spellingShingle | Nabaraj Adhikari Wutiphol Sintunavarat A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach Results in Control and Optimization Quaternion Julia sets Quaternion Mandelbrot sets Viscosity approximation method Escaping criterion |
| title | A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach |
| title_full | A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach |
| title_fullStr | A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach |
| title_full_unstemmed | A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach |
| title_short | A novel investigation of quaternion Julia and Mandelbrot sets using the viscosity iterative approach |
| title_sort | novel investigation of quaternion julia and mandelbrot sets using the viscosity iterative approach |
| topic | Quaternion Julia sets Quaternion Mandelbrot sets Viscosity approximation method Escaping criterion |
| url | http://www.sciencedirect.com/science/article/pii/S2666720725000116 |
| work_keys_str_mv | AT nabarajadhikari anovelinvestigationofquaternionjuliaandmandelbrotsetsusingtheviscosityiterativeapproach AT wutipholsintunavarat anovelinvestigationofquaternionjuliaandmandelbrotsetsusingtheviscosityiterativeapproach AT nabarajadhikari novelinvestigationofquaternionjuliaandmandelbrotsetsusingtheviscosityiterativeapproach AT wutipholsintunavarat novelinvestigationofquaternionjuliaandmandelbrotsetsusingtheviscosityiterativeapproach |