A Four Step Feedback Iteration and Its Applications in Fractals
Asifa Tassaddiq, Muhammad Tanveer, Muhammad Azhar, Waqas Nazeer, Sania Qureshi
Abstract
Fractals play a vital role in modeling the natural environment. The present aim is to investigate the escape criterion to generate specific fractals such as Julia sets, Mandelbrot sets and Multi-corns via F-iteration using complex functions h(z)=zn+c, h(z)=sin(zn)+c and h(z)=ezn+c, n≥2,c∈C. We observed some beautiful Julia sets, Mandelbrot sets and Multi-corns for n = 2, 3 and 4. We generalize the algorithms of the Julia set and Mandelbrot set to visualize some Julia sets, Mandelbrot sets and Multi-corns. Moreover, we calculate image generation time in seconds at different values of input parameters.
Topics & Concepts
Mandelbrot setJulia setFractalSet (abstract data type)MathematicsComplex quadratic polynomialNewton fractalDiscrete mathematicsCombinatoricsAlgorithmComputer scienceMathematical analysisIterative methodPolynomialProgramming languageLocal convergenceMathematical Dynamics and FractalsOptimization and Variational AnalysisMorphological variations and asymmetry