A new method for calculating fractal dimension is developed in this paper. The method is based on the box dimension concept; however, it involves direct estimation of a suboptimal covering of the data set of interest. By finding a suboptimal cover, this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm. ...

holds, then f is called a generalized convex function on I []. In α = , we have convex function, convexity is defined only in geometrical terms as being the property of a function whose graph bears tangents only under it []. The convexity of functions plays a significant role in many fields, for example, in biological system, economy, optimization, and so on [–]. In recent years, the fract...

There were great expectations in the 1980s in connection with the practical applications of mathematical processes which were built mainly upon Fractal Dimension (FD) mathematical basis. Significant results were achieved in the 1990s in practical applications in the fields of information technology, certain image processing areas, data compression, and computer classification. In the present pu...

many studies suggested that fractals could be brought in any structural anarchy, such as cancers, for diagnosis and prognosis evaluation by quantifying it and expressing it in terms of fractal geometry. in this study, we aimed to evaluate pathologic grades or breast carcinomas by fractal analysis. this cross-sectional study was performed on 60 women with breast ductal carcinoma. from all the pa...

This article reports on the application of the recently introduced concept of multiscale fractal dimension (MFD) as a resource for quantifying three-dimensional gene expression patterns in embryonic development. While traditional fractal dimensions provide interesting possibilities for quantifying pattern complexity, as defined by the intensity in which the pattern interacts with its surroundin...

This thesis examines the concept of image self-similarity and provides solutions to various associated inverse problems such as resolution enhancement and missing fractal codes. In general, many real-world inverse problems are ill-posed, mainly because of the lack of existence of a unique solution. The procedure of providing acceptable unique solutions to such problems is known as regularizatio...

The theory that ties normal functioning and pathology of the brain and visual system with the spatial-temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or...