We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. This characterizes all countable fundamental groups for planar Rauzy fractals. We give an explicit construction relying on two operations on substitutions: symbolic splittings and conjugations by free group automorphisms.

An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS) modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biomet...

Many morphometric approaches have been proposed for quantitative evaluation of alveolarization in experimental models of bronchopulmonary dysplasia (BPD), such as alveolar number, alveolar size and variability, mean linear intercept (Lm), surface-to-volume ratio, or radial alveolar count. Conversely, no papers are available about potentiality of fractal analysis in this matter. Thus, in the pre...

Heat transfer by electromagnetic radiation is one of the common methods of energy transfer between objects. Using the fluctuation-dissipation theorem, we have studied the effect of particle arrangement in the transmission of radiative heat in many-body systems. In order to show the effect of the structure morphology on the collective properties, the radiative heat transfer is studied and the re...

We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. This characterizes all countable fundamental groups for planar Rauzy fractals. We give an explicit construction relying on two operations on substitutions: symbolic splittings and conjugations by free group automorphisms.

background & objectives: cancer is a serious problem for human being and is becoming a serious problem day-by-day .a prerequisite for any therapeutic modality is early diagnosis. automated cancer diagnosis by automatic image feature extraction procedures can be used as a feature extraction in the field of fractal dimension. the aim of this survey was to introduce a quantitative and objectiv...

INTRODUCTION Cervical intraepithelial neoplasias (CIN) represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN) and its fractal dimension was investigated to establish a basis for an objective diagnosis ...

On the basis of the analysis of random pulse signal, the mathematical model of the two-parameter random signal is established. Based on which, it is found that the random signal has a non-integer dimension fractal characteristics, and the fractal dimension is the ratio of the count distribution and the number of discrete degree ln σ . Besides, the mass distribution of the particle group is also...