On Generating Julia Set Fractal Shaped Images through Mobius Transformations

On Generating Julia Set Fractal Shaped Images through Mobius Transformations

1. Bourke, P.: An Introduction to fractals ,http://paulbourke.net/fractals/fracintro/ 2. Gangopadhyay, T. The effect of multiple rotations on Mobius transformations in generating IFS Fractalss, International journal of Computer Applications 142(6):18-22, May 2016 3. Julia, G. Mémoire sur l'itération des fonctions rationnelles, Journal de Mathématiques Pures et Appliquées, 1918 4. Krantz, S. G. ...

Parametric 2-dimensional L systems and recursive fractal images: Mandelbrot set, Julia sets and biomorphs

The Effect of Multiple Rotations on Mobius Transformations in Generating IFS Fractals

1. Bourke, P.: An Introduction to the Apollony Fractal. Computers and Graphics, 30( 2006) 134–136. 2. Gangopadhyay, T. IFS Fractals generated by Affine Transformation with Trigonometric Coefficients and their Transformations, International journal of Computer Applications 53(2012) 29-32.. 3. Gangopadhyay, T. The Effect of Multiple Rotations on a Unified System of Affine Transformations with Rel...

Generation of 3D Fractal Images for Mandelbrot and Julia Sets

Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invariance, and dimensionality. Images such as coastlines, terrains, cloud mountains, and most interestingly, random shapes composed of curves, sets of curves, etc. present a multivaried spectrum of fractals usage in ...

Laplacians on the Basilica Julia Set

We consider the basilica Julia set of the polynomial P (z) = z − 1 and construct all possible resistance (Dirichlet) forms, and the corresponding Laplacians, for which the topology in the effective resistance metric coincides with the usual topology. Then we concentrate on two particular cases. One is a self-similar harmonic structure, for which the energy renormalization factor is 2, the expon...