Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations
We explore some new variants of the Julia set by developing the escape criteria for a function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">sin</mo><mo>(<...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/4/272 |
| _version_ | 1827672391584579584 |
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| author | Swati Antal Anita Tomar Darshana J. Prajapati Mohammad Sajid |
| author_facet | Swati Antal Anita Tomar Darshana J. Prajapati Mohammad Sajid |
| author_sort | Swati Antal |
| collection | DOAJ |
| description | We explore some new variants of the Julia set by developing the escape criteria for a function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">sin</mo><mo>(</mo><msup><mi>z</mi><mi>n</mi></msup><mo>)</mo><mo>+</mo><mi>a</mi><mi>z</mi><mo>+</mo><mi>c</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>,</mo><mi>c</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>, and <i>z</i> is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the impact of parameters on the deviation of dynamics, color, and appearance of fractals. Some of these fractals represent the stunning art on glass, and Rangoli (made in different parts of India, especially during the festive season) which are useful in interior decoration. Some fractals are similar to beautiful objects found in our surroundings like flowers (to be specific Hibiscus and Catharanthus Roseus), and ants. |
| first_indexed | 2024-03-10T04:05:46Z |
| format | Article |
| id | doaj.art-e62f1a5692834f5796e903f444630e8d |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:46Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e62f1a5692834f5796e903f444630e8d2023-11-23T08:24:40ZengMDPI AGFractal and Fractional2504-31102021-12-015427210.3390/fractalfract5040272Fractals as Julia Sets of Complex Sine Function via Fixed Point IterationsSwati Antal0Anita Tomar1Darshana J. Prajapati2Mohammad Sajid3BGR Campus, Hemavati Nandan Bahuguna Garhwal University, Pauri Garhwal 246001, IndiaPt. L.M.S. Campus, Sri Dev Suman Uttrakhand University, Rishikesh 249201, IndiaM.B. Patel Institute of Technology, New Vallabh Vidyanagar 388121, IndiaDepartment of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi ArabiaWe explore some new variants of the Julia set by developing the escape criteria for a function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">sin</mo><mo>(</mo><msup><mi>z</mi><mi>n</mi></msup><mo>)</mo><mo>+</mo><mi>a</mi><mi>z</mi><mo>+</mo><mi>c</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>,</mo><mi>c</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>, and <i>z</i> is a complex variable, utilizing four distinct fixed point iterative methods. Furthermore, we examine the impact of parameters on the deviation of dynamics, color, and appearance of fractals. Some of these fractals represent the stunning art on glass, and Rangoli (made in different parts of India, especially during the festive season) which are useful in interior decoration. Some fractals are similar to beautiful objects found in our surroundings like flowers (to be specific Hibiscus and Catharanthus Roseus), and ants.https://www.mdpi.com/2504-3110/5/4/272escape criterionfixed pointMann orbitIshikawa orbitNoor orbit |
| spellingShingle | Swati Antal Anita Tomar Darshana J. Prajapati Mohammad Sajid Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations Fractal and Fractional escape criterion fixed point Mann orbit Ishikawa orbit Noor orbit |
| title | Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations |
| title_full | Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations |
| title_fullStr | Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations |
| title_full_unstemmed | Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations |
| title_short | Fractals as Julia Sets of Complex Sine Function via Fixed Point Iterations |
| title_sort | fractals as julia sets of complex sine function via fixed point iterations |
| topic | escape criterion fixed point Mann orbit Ishikawa orbit Noor orbit |
| url | https://www.mdpi.com/2504-3110/5/4/272 |
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