Numeric characteristics of generalized M-set with its asymptote
Article
Liu, S., Cheng, X., Fu, W., Zhou, Y. and Li, Q. 2014. Numeric characteristics of generalized M-set with its asymptote. Applied Mathematics and Computation. 243, pp. 767-774. https://doi.org/10.1016/j.amc.2014.06.016
| Type | Article |
|---|---|
| Title | Numeric characteristics of generalized M-set with its asymptote |
| Authors | Liu, S., Cheng, X., Fu, W., Zhou, Y. and Li, Q. |
| Abstract | The Mandelbrot set (M-set) formulated by fc(z) = z2 + c is important in chaos theory. It has been extended into generalized M set (k-M set) fc(z) = zk + c by using different exponent k. The escape time algorithm is used to draw fractals, which need preset thresholds and a maximum iteration times as input. This paper presents and proves the upper and lower bounds of generalized M set thresholds. A new method is also introduced to draw k-M set when k is a rational number. This method uses asymptotes of k-M set to approach k-M set from the outside. We prove that k-M set is the limit of these asymptotes. Finally, some experiments are presented to validate our methods. |
| Keywords | Fractal; Mandelbrot set; Generalized Mandelbrot set; Rational exponent; Asymptote |
| Publisher | Elsevier |
| Journal | Applied Mathematics and Computation |
| ISSN | 0096-3003 |
| Electronic | 0096-3003 |
| Publication dates | |
| Online | 07 Jul 2014 |
| 15 Sep 2014 | |
| Publication process dates | |
| Deposited | 09 Jul 2018 |
| Accepted | 01 Jan 2014 |
| Output status | Published |
| Digital Object Identifier (DOI) | https://doi.org/10.1016/j.amc.2014.06.016 |
| Web of Science identifier | WOS:000340563800073 |
| Language | English |
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