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Due to their practicality and convenient parametrization, fractals derived from iterated function systems (IFSs) constitute powerful tools widely used to model natural and synthetic shapes. An IFS can generate sets other than fractals, extending its application field. Some of such sets arise from IFS fractals by adding minimal modifications to their defining rule. In this work, we propose two modifications to a fractal recently introduced by the authors: the so-called 2 -ball fractal dust, which consists of a set of balls diminishing in size along an iterative process and delimited by an enclosing square. The proposed modifications are (a) adding a resizer parameter to introduce an interaction between the generator and generated ball elements and (b) a new fractal embedded into the 2 -ball fractal dust, having the characteristic of filling zones not covered by the previous one. We study some numerical properties of both modified resulting sets to gain insights into their general properties. The resulting sets are geometrical forms with potential applications. Notably, the first modification generates an algorithm capable of producing geometric structures similar to those in mandalas and succulent plants; the second modification produces shapes similar to those found in nature, such as bubbles, sponges, and soil. Then, although a direct application of our findings is beyond the scope of this research, we discuss some clues of possible uses and extensions among which we can remark two connections: the first one between the parametrization we propose and the mandala patterns, and the second one between the embedded fractal and the grain size distribution of rocks, which is useful in percolation modeling. [ABSTRACT FROM AUTHOR]

Due to their practicality and convenient parametrization, fractals derived from iterated function systems (IFSs) constitute powerful tools widely used to model natural and synthetic shapes. An IFS can generate sets other than fractals, extending its application field. Some of such sets arise from IFS fractals by adding minimal modifications to their defining rule. In this work, we propose two modifications to a fractal recently introduced by the authors: the so-called 2-ball fractal dust, which consists of a set of balls diminishing in size along an iterative process and delimited by an enclosing square. The proposed modifications are (a) adding a resizer parameter to introduce an interaction between the generator and generated ball elements and (b) a new fractal embedded into the 2-ball fractal dust, having the characteristic of filling zones not covered by the previous one. We study some numerical properties of both modified resulting sets to gain insights into their general properties. The resulting sets are geometrical forms with potential applications. Notably, the first modification generates an algorithm capable of producing geometric structures similar to those in mandalas and succulent plants; the second modification produces shapes similar to those found in nature, such as bubbles, sponges, and soil. Then, although a direct application of our findings is beyond the scope of this research, we discuss some clues of possible uses and extensions among which we can remark two connections: the first one between the parametrization we propose and the mandala patterns, and the second one between the embedded fractal and the grain size distribution of rocks, which is useful in percolation modeling.

The concept of the fractal approach is discussed in relation to the description of some properties of dilute aqueous solutions and suspensions of low concentrations. The role of weakly interacting objects in the form of van der Waals interactions in the properties of biological objects in the aquatic environment is considered. A model is proposed in which the observed dependences are represented by small differences in the dielectric constant. Biological particles are modeled as water balls with a slightly higher refractive index, moving against a background of clear water. The van der Waals theory is used to calculate the average relative distance between spheres in the approximation of a small distance, and physically reasonable results are found. [ABSTRACT FROM AUTHOR]

Microcalcifications (μCas) are often early signs of breast cancer. However, detecting them is a difficult visual task and recognizing malignant lesions is a complex diagnostic problem. In recent years, several research groups have been working to develop computer-aided diagnosis (CAD) systems for X-ray mammography. In this paper, we propose a method to detect and classify microcalcifications. In order to discover the presence of μCas clusters, particular attention is paid to the analysis of the spatial arrangement of detected lesions.A fractal model has been used to describe the mammographic image, thus, allowing the use of a matched filtering stage to enhance microcalcifications against the background. A region growing algorithm, coupled with a neural classifier, detects existing lesions. Subsequently, a second fractal model is used to analyze their spatial arrangement so that the presence of microcalcification clusters can be detected and classified.Reported results indicate that fractal models provide an adequate framework for medical image processing; consequently high correct classification rates are achieved. [Copyright &y& Elsevier]