Back to Search
Start Over
On the Connectivity Measurement of the Fractal Julia Sets Generated from Polynomial Maps: A Novel Escape-Time Algorithm
- Source :
- Fractal and Fractional, Volume 5, Issue 2, Fractal and Fractional, Vol 5, Iss 55, p 55 (2021)
- Publication Year :
- 2021
- Publisher :
- Multidisciplinary Digital Publishing Institute, 2021.
-
Abstract
- In this paper, a novel escape-time algorithm is proposed to calculate the connectivity’s degree of Julia sets generated from polynomial maps. The proposed algorithm contains both quantitative analysis and visual display to measure the connectivity of Julia sets. For the quantitative part, a connectivity criterion method is designed by exploring the distribution rule of the connected regions, with an output value Co in the range of [0,1]. The smaller the Co value outputs, the better the connectivity is. For the visual part, we modify the classical escape-time algorithm by highlighting and separating the initial point of each connected area. Finally, the Julia set is drawn into different brightnesses according to different Co values. The darker the color, the better the connectivity of the Julia set. Numerical results are included to assess the efficiency of the algorithm.
- Subjects :
- Statistics and Probability
Polynomial
Computer science
MathematicsofComputing_GENERAL
Value (computer science)
Julia sets
01 natural sciences
Measure (mathematics)
010305 fluids & plasmas
Fractal
0103 physical sciences
QA1-939
010301 acoustics
QA299.6-433
Degree (graph theory)
Statistical and Nonlinear Physics
Julia set
Range (mathematics)
fractals
connectivity
Thermodynamics
escape-time algorithm
QC310.15-319
Algorithm
Mathematics
Analysis
Distribution rule
Subjects
Details
- Language :
- English
- ISSN :
- 25043110
- Database :
- OpenAIRE
- Journal :
- Fractal and Fractional
- Accession number :
- edsair.doi.dedup.....cbc112815e7bd5e05894c0164ff31983
- Full Text :
- https://doi.org/10.3390/fractalfract5020055