Some necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Some generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal proper...

MOTIVATION The importance of a systematic methodology for the mathematical characterization of three-dimensional gene expression patterns in embryonic development. METHODS By combining lacunarity and multiscale fractal dimension analyses with computer-based methods of three-dimensional reconstruction, it becomes possible to extract new information from in situ hybridization studies. Lacunarit...

Abstract—A miniaturized printed log-periodic fractal dipole antenna is proposed. Tree fractal structure is introduced in an antenna design and evolves the traditional Euclidean log-periodic dipole array into the log-periodic second-iteration tree-dipole array (LPT2DA) for the first time. Main parameters and characteristics of the proposed antenna are discussed. A fabricated proof-of-concept pro...

As evidence from recent years has demonstrated, box-counting provides an objective fractal analytical method to evaluate the visual complexity of architecture. This paper for the first time explores the potential of box-counting with regard to the work of the Viennese architect Adolf Loos (1870-1933). Loos is seen as the pioneer of modern architecture, as someone who anticipated the Internation...

We consider the problem of decoding block coded data, using a physical dynamical system. We sketch out a decompression algorithm for fractal block codes and then show how to implement a recurrent neural network using physically simple but highly-nonlinear, analog circuit models of neurons and synapses. The nonlinear system has many fixed points, but we have at our disposal a procedure to choose...

This paper introduces a new concept for interface based on user perception, according to its definition in phenomenology framework. Based on studies about fractal aesthetics and its effect in human perception, an analogy is made with the scale-free topology of collaborative networks. Properties of this scale invariance characteristic should then be used for a computational implementation of a d...

Nonlinear dynamics, a branch of the basic sciences that studies complex physical systems, offers novel approaches to long-standing problems of physiological form and function. The nonlinear concept of fractals, introduced and developed over the last decade, provides insights into the organization of complex structures such as the tracheobronchial tree and heart, as well as into the dynamics of ...

A novel fractal antenna-array type is proposed. The design is based on the Sierpinski rectangular carpet concept. However, the generator is a circular ring area, filled with radiating elements, so the higher stages of the fractal development produce large arrays of circular rings which, besides the high directivity, have the advantage of the almost uniform azimuthal radiation pattern, attribute...

In this paper, a novel method for edge detection of microcalcification clusters in mammogram images is presented using the concept of Fractal Dimension and Hurst co-efficient that enables to locate the microcalcifications in the mammograms. This technique detects the edges accurately than the ones obtained by the conventional Sobel method. Generally, Sobel method detects the edges of the region...