Enhancing Computational Thinking with Spreadsheet and Fractal Geometry: Part 3 Mandelbrot and Julia Set

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

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 ...

The Complex Geometry of the Mandelbrot Set

In this paper, we give a brief overview of the geometry of the Mandelbrot set. We show how to distinguish each of the principal bulbs hanging off the main cardioid of this set by counting the spokes of the antennas attached to each bulb. We also use these antennas to attach a fraction to each such bulb, and this then indicates how these bulbs are arranged around the boundary of the main cardioid.

the differential effects of debate and media analysis as relate to enhancing efl learners critical thinking ability and writing performances

critical thinking ability has an important role in education. accordingly, scholars around the world are searching for new ways for teaching and improving students critical thinking ability. in line with the studies in efl contexts supporting the positive relationship between critical thinking and writing performances, this study investigated the differential effects of halverson’s critical thi...

Notes on Tan ’ s theorem on similarity between the Mandelbrot set and the Julia sets ∗

This note gives a simplified proof of the similarity between the Mandelbrot set and the quadratic Julia sets at the Misiurewicz parameters, originally due to Tan Lei [TL]. We also give an alternative proof of the global linearization theorem of repelling fixed points. 1 Simlarity between M and J We first give a proof of Tan’s theorem, in a way inspired by Schwick [Sch]. The Julia sets and the M...