This paper examines the fractal nature of the Narayana fractal, an object defined by N = {(i, j) ∈ N× N : N(i + j + 1, j + 1) = 1 (mod 2)}. where N(n, k) = 1 n ( n k )( n k − 1 ) are the Narayana numbers. This object closely resembles a fractal derived from Pascal’s triangle. This similarity is used to prove that the Hausdorff dimension of the Narayana fractal is log 3/ log 2, and the limit of ...

The fractal image compression technique models a natural image using a contractive mapping called fractal mapping in the image space. In this paper, we demonstrate that the fractal image coding algorithm is compatible with other image coding methods. In other words, we can encode only part of the image using fractal technique and model the remaining part using other algorithms. According to suc...

To better understand the characteristics of seepage-pores (pore radius larger than 100 nanometers) and their influence on the permeability of coals, we have conducted fractal analyses for 34 fresh coal samples (mean maximum vitrinite reflectance Ro,max from 0.43% to 4.21%) from North, Northwest and Northeast China. Mercury porosimetry data indicate that the coals are fractal, with pore radius r...

In this paper, we implemented both sequential and parallel version of fractal image compression algorithms using CUDA (Compute Unified Device Architecture) programming model for parallelizing the program in Graphics Processing Unit for medical images, as they are highly similar within the image itself. There are several improvement in the implementation of the algorithm as well. Fractal image c...

OBJECTIVE Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. RESEARCH DESIGN AND METHODS We conducted a cross-sectional study ...

To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the m...

Fractal is a tool in data fitness and interpolation. It’s better to fit complex graphs. But optimization of fitness has proven to be a challenging problem in application of fractal. In this paper, a description of a genetic algorithm (GA) and the software written to optimize effect on self-affine fractal interpolation function (AFIF) implement is given. The software developed was tested on real...

Since the end of the Seventies, following work of the French mathematician Mandelbrot, We are witnessing the true exploitation of the interest expressed by the scientific community for the fractals objects. The aim of this paper is to introduce the fractal theory by the calculation of the fractal dimension in the radiographic images. We implement for that, the box counting method for the segmen...

In this paper, the basic theory of image fractal compression is briefly introduced; some typical fractal compression approaches are discussed. Based on this discussion, according to the problem of long encoding time which exists in the typical fractal compression approaches, we propose a fast image fractal compression approach based on the combination of adaptive quad tree compression approach ...

TCP traffic has been reported to have not only self-similarity but multi-fractal nature. Multi-fractal nature of traffic volume, in general, is well known to have significant influence to queueing behavior in short time scale. In the paper, we investigate about ”what component of TCP congestion control mechanism affects to multifractal nature of generated traffic?”. We artificially divide TCP c...