We report an algorithm for the partition of a line segment according to a given ratio ν. At each step the length distribution among sets of the partition follows a binomial distribution. We call k-set to the set of elements with the same length at the step n. The total number of elements is 2 and the number of elements in a same k-set is C n. In the limit of an infinite partion this object beco...

Parkinson’s disease (PD) and basal ganglia dysfunction impair movement timing, which leads to gait instability and falls. Parkinsonian gait consists of random, disconnected stride times— rather than the 1/f structure observed in healthy gait—and this low fractal scaling of stride times is a strong predictor of falling. Walking with fixed-tempo Rhythmic Auditory Stimulation (RAS) improves many a...

We derive a new lower bound p c > 0:8107 for the critical value of Mandelbrot's dyadic fractal percolation model. This is achieved by taking the random fractal set (to be denoted A 1) and adding to it a countable number of straight line segments, chosen in a certain (non-random) way as to simplify greatly the connectivity structure. We denote the modiied model thus obtained by C 1 , and write C...

We study the fractal and multifractal properties (i.e., the generalized dimensions of the harmonic measure) of a two-parameter family of growth patterns that result from a growth model that interpolates between diffusion-limited aggregation (DLA) and Laplacian growth patterns in two dimensions. The two parameters are beta that determines the size of particles accreted to the interface, and C th...

The microstructure of calcium-silicate-hydrate (C-S-H) gel, a major hydrated phase of Ordinary Portland Cement, with and without polycarboxylic ether (PCE) additives is investigated by combined analyses of small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) data. The results show that these comb-shaped polymers tend to increase the size of the disk-like globules but ha...

1 I n t r o d u c t i o n The aim of geometric modeling is to model forms by manipulating or combining well-known shapes such as circles and boxes. In order to be convenient such a model should allow easy control and manipulation of the final shape. When dealing with fractal geometric modeling, the control on ffactal figures is not so easily achieved as with classical smooth ones. The difficult...

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. ...

Abstract Identifying geological characteristics such as rock types and fractures is an important step in fractured reservoirs’ modeling developing oil gas fields. The productivity index (PI) essential parameter for this purpose. There are different methods separating identifying fractures, including simple statistical complex fractal based on the spatial structure of data. In study, areas were ...

Fractal dimension is an important tool for the analysis of medical images. MR images and the mammographic images give a detailed view of both benign and malignant lesions. This work focuses on the extraction of boundary and analysis of its fractal dimensions to classify the benign and malignant lesions. The boundary of the lesion is extracted using fuzzy c-means clustering. The lesion contour i...