We show how students’ response patterns can be quantified both globally and locally using the concept of fractal dimension. This metric allows us to identify students who respond to a series of questions and problems in a persistent or anti-persistent manner with implications for personalized just-in-time teaching and learning.

Despite the lack of empirical evidence some presocratic Greek thinkers did not hesitate to speculate on a spacially infinite universe. This should not come as a surprise, since the idea of infinite appears tightly bound with the concept of an universe, though not necessarily with the construct of the cosmos. Ancient thinkers did not reach this idea easily, however, since the concept did not app...

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of t...

In this article, one defines two models of adaptive systems: the metadynamical adaptive system using the notion of Kalman dynamical systems and the adaptive differential equations using the notion of variable dimension spaces. This concept of variable dimension spaces relates the notion of spaces to the notion of dimensions. First, a computational model of the Douady’s Rabbit fractal is obtaine...

In this work, the analysis of a tree-inspired fractal structure is presented. First, trajectories of points on branches of different hierarchy of a tree that oscillates freely are recorded in experiments. Then, the principle axes and ellipses of displacements are determined analytically for a sympodial fractal mechanical model. Modes of oscillations and their frequencies are found numerically f...

The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is...

In this work, SiO2 –ZrO2 mixed oxides was prepared by the polymeric sol–gel route. The characterization of pore structure, which determines the permeation process of membrane, is of great importance. So far, most investigations have focused on such pore structure as specific surface area and pore size distribution, but the surface fractal, the important parameter reflecting the roughness of por...

We introduce a new way to use fractal coding for image compression, based on the parallel use of a fractal encoder and a DCT encoder. The two encoders are given the complementary roles to capture the information of edge and smooth variation, and the information of detail respectively. We show the advantage of using this hybrid coding scheme over the use of a fractal encoder alone, or a DCT enco...

The immense use of the images in the field of communication and animation drives the attention towards an important concept i.e. compression, because of compactness and restricted size for the data storage. From last few years a continuous development is going on in the field of compression. For still image compression JPEG is used world -wide. But other methods are also being explored; Fractal...