ion level high low Fig. 1. Generations of triadic Koch curve. By changing the scale, its abstraction level also changes. 1). This approximation, by changing the scale, can also be seen when we process digital images and so on. We call this approximation mechanism fractal views. The information structures used in computers, such as the directory structure of UNIX 2 , are generally represented as...

The fractal geometry, issued of a synthesis of works done in Mathematics and in Physics since more of one century, proposed in the 70’s new concepts to understand some complex phenomenon ([Man77]). The notions of fractional dimension and scale invariance have been recognized applicable quickly for the description of many natural objects, of the mountainous to the maritime facades while passing ...

Seafloor topographic complexity is ecologically important because it provides habitat structure and alters boundary-layer flow over the bottom. Despite its importance, there is little agreement on how to define and measure surface complexity. The purpose of this investigation was to utilize fractal geometry of vertical cross-section profiles to characterize the surface topography of the soft-bo...

Language entails many nested time scales, ranging from the relatively slow scale of cultural evolution to the rapid scale of individual cognition. The nested, multiscale nature of language implies that even simple acts of text production, such as typing a sentence, entail complex interactions involving multiple concurrent processes. As such, text production may have much in common with other co...

Compelling evidence exists to show that the structure of molecular clouds is fractal in nature. In this poster, the author reiterates that view and, in addition, asserts that not only is cloud geometry fractal, but that they also have a common characteristic they are similar in shape to the Horsehead in Orion. This shape can be described by the Julia function f(z) = z + c,where both z and c are...

Nature has inspired many scientists and engineers to solve problems through observation and mimicry. One such example is heat transfer enhancement. The enormous natural heat and mass transfer phenomena have led engineers to seek solutions to heat transfer enhancement problems from nature. Fractal geometries are found in respiratory and vascular systems of plants and animals, such as blood vesse...

The concept of atomic weights (relative atomic masses) of chemical elements and molecular weights (relative molecular masses) of chemical compounds is fundamental to chemistry and the problem to determine their values has captured attention of chemists for a long time. On the other hand, fractal ideas of Mandelbrot have been extended to studies of various forms in nature on a wide range of leng...

Beginning with the most general fractal strings/sprays construction recently expounded in the book by Lapidus and Frankenhuysen, it is shown how the complexified extension of El Naschie’s CantorianFractal spacetime model belongs to a very special class of families of fractal strings/sprays whose scaling ratios are given by suitable pinary (pinary, p prime) powers of the Golden Mean. We then pro...

Streamlines are a popular way of visualizing flow in vector fields. A major challenge in flow field visualization is selecting the streamlines to view. Rendering too many streamlines clutters the visualization and makes features of the field difficult to identify. Rendering too few streamlines causes viewers to completely miss features of the flow field not rendered. The fractal dimension of a ...

Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure ...