Fractals Generated by Various Iterative Procedures – A Survey

These days fractals and the study of their dynamics is one of the emerging and interesting area for mathematicians. New fractals for various equations have been created using one-step iterative procedure, two-step iterative procedure, three-step iterative procedure and four-step iterative procedure in the literature. Fractals are geometric shapes that have symmetry of scale. In this paper, a detailed survey of fractals existing in the literature such as Julia sets, Mandelbrot sets, Cantor sets, etc have been given

African fractals as a tool for transformative education in Africa

Nature is replete with repetitive patterns in diminishing scales. Similarly, cultures produce recursive patterns that characterize their specific social, cultural, economic and political organisation. These self-similar, variously scaled and mostly infinitive patterns are called fractals. The uniqueness of African fractals emanates from the culture of the African peoples. Particular elements of these fractals have contributed immensely in mathematical learning especially in modern computing. This paper contends that the inclusion of African fractal education in curricula at all levels in Africa have the potential to contribute to better understanding of African identity, and promote African centred education that forestalls the alienation of the African from their environment. The paper argues that the teaching of African fractals in Africa is a needed project to facilitate understanding of the intricacies between nature and humans. It should deepen understanding about the concept of embedded humanity expressed in ideas of Ubuntu; and help awaken African consciousness about possibilities beyond empiricism. Recommendations are made on ways to include African fractals in the syllabus in Africa using the Ghana’s pre-tertiary level (Senior High School) as an example

The Fractal Geometry of Mathematics Classrooms: Navigating Classroom Environments in Factory-Model Schools

Mathematics education has a diverse and complex history. After decades of national reform, mathematics classrooms today are still in desperate need of change. This article examines the current state of factory-model schooling through the lens of Mandelbrot\u27s The Fractal Geometry of Nature in order to rethink pedagogic practices

Fractals and music

Many natural phenomena we find in our surroundings, are fractals.  Studying and learning about fractals in classrooms is always a challenge for both teachers and students. We here show that the sound of musical instruments can be used as a good resource in the laboratory to study fractals. Measurement of fractal dimension which indicates how much fractal content is there, is always uncomfortable, because of the size of the objects like coastlines and mountains. A simple fractal source is always desirable in laboratories. Music serves to be a very simple and effective source for fractal dimension measurement. In this paper, we are suggesting that music which has an inherent fractal nature can be used as an object in classrooms to measure fractal dimensions. To find the fractal dimension we used the box-counting method. We studied the sound produced by different stringed instruments and some common noises. For good musical sound, the fractal dimension obtained is around 1.6882

Fractals

Volume 3, Issue 1, January 201