Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical propertie...

In this paper we address two issues in modeling natural terrain using fractal geometry: estimation of fractal dimension, and fractal surface reconstruction. For estimation of fractal dimension, we extend the fractal Brownian function approach to accommodate irregularly sampled data, and we develop methods for segmenting sets of points exhibiting self-similarity over only certain scales. For fra...

Fractal shaped antennas and fractal miniaturized elements are becoming a promising new family of devices with a wealth of potentially useful applications [1]. Owing to the facility of manufacturing fractal devices (the metallisation process of fractal antennas up to a few iterations of the recursive process that generates the fractal structure is a relatively simple task), several different pro...

In this paper we have defined two functions that have been used to construct different fractals having fractal dimensions between 1 and 2. More precisely, we can say that one of our defined functions produce the fractals whose fractal dimension lies in [1.58, 2) and rest function produce the fractals whose fractal dimension lies in (1, 1.58]. Also we tried to calculate the amount of increment o...

sciences exist to demonstrate the fundamental order underlying nature. chaos/complexity theory is a novel and amazing field of scientific inquiry. notions of our everyday experiences are somehow in connection to the laws of nature through chaos/complexity theory’s concerns with the relationships between simplicity and complexity, between orderliness and randomness (retrieved from http://www.inc...

Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to eit...

We use the fractional integrals to describe fractal solid. We suggest to consider the fractal solid as special (fractional) continuous medium. We replace the fractal solid with fractal mass dimension by some continuous model that is described by fractional integrals. The fractional integrals are considered as approximation of the integrals on fractals. We derive fractional generalization of the...