The observation that natural curves and surfaces are often fractal suggests that people may be sensitive to their statistical properties. The perceptual protocols that underlie discrimination between fractals and between other types of random contour and fractals are examined. Discrimination algorithms that have precisely the same sensitivities as human observers are constructed. These algorith...

A lot of formal and informal recreational study took place in the fields of Meromorphic Maps, since Mandelbrot popularized the map z ← z + c. An immediate generalization of the Mandelbrot z ← z + c also known as the Multibrot family were also studied. In the current paper, general truncated polynomial maps of the form z ← ∑ p≥2 apx p + c are studied. Two fundamental properties of these polynomi...

But even the very hairs of your head are all numbered. Fear not therefore: ye are of more value than many sparrows. shows that valuations are useful not only within the theory of codes, but also when dealing with ambiguity, especially in contextfree grammars, or for deening outer measures on the space of !-words which are of some importance to the theory of fractals. These connections yield new...

In this paper we have defined one function that has been used to construct different fractals having fractal dimensions between 1.58 and 2. Also, we tried to calculate the amount of increment of fractal dimension in accordance with the base of the number systems. Further, interestingly enough, these very fractals could be a frame of lyrics for the musicians, as we know that the fractal dimensio...

The engineering properties of particulate materials are the collective manifestation interactions among their constituent particles and structures within which adopt spatial arrangement. For first time in literature, this paper employs an extended concept ‘fractals’ to show that constituting a certain size can be rationalized three universal fractals. Within each fractal, build repeatable, repr...

<p style='text-indent:20px;'><i>Fractals</i> in higher dimensional <i>dynamical systems</i> have significant roles physics and other applied sciences. In this paper, one of the key property fractals, called <i>self similarity</i> product systems, is studied using concept <i>similarity boundary</i>. The relationship between similarity boundar...

Fractal, which means broken or irregular fragments, was originally coined by Dr B. Mandelbrot in the year the 1970. Fractals describe a family of complex shapes that possess an inherent self-similarity in their geometrical structure usually in nature, since the pioneering work of Mandelbrot and others, a wide variety of applications for fractals has been found in many branches of science and en...

Fractal structures appear in a vast range of physical systems. A literature survey including all experimental papers on fractals which appeared in the six Physical Review journals ~A–E and Letters! during the 1990s shows that experimental reports of fractal behavior are typically based on a scaling range D that spans only 0.5–2 decades. This range is limited by upper and lower cutoffs either be...

APPLICATION OF FRACTALS TO MATERIALS SCIENCE Introduction The term “Fractals” refers to the mathematical concept of how vastly different objects can be described using the same mathematical relationships. For example, the coastline of a continent viewed from space will have readily visible distinct attributes such as bays, peninsulas, and relatively straight sections. If we now observe a coastl...

The scaling behavior of linear polymers in disordered media, modelled by self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by numerical simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our numerical results yield estimates of critical exponents, governing the scaling laws of disorder averages of the co...