We measure the fractal dimension of an African plant that is widely cultivated as ornamental, the Asparagus plumosus. This plant presents self-similarity, remarkable in at least two different scalings. In the following, we present the results obtained by analyzing this plant via the box counting method for three different scalings. We show in a quantitatively way that this species is a fractal.

Fractal scaling behavior of long-term records of daily runoff time series in 31 sub-watersheds covering a wide range of size were examined using the shifted box-counting method and Hurst rescaled range (R/S) analysis. These subwatersheds were associated with four agricultural watersheds of different climate and topography. The results showed that the records of daily runoff rate exhibited scale...

Fractal dimension can be used to describe the self-similarity, the complexity, or the irregularity of images. One of the most popular ways to estimate the fractal dimension of images is the box-counting method (BCM). Its naive estimates, however, tend to be inaccurate. This paper gives careful consideration to the sources of inaccurate estimates and modifies Buczkowski's method for accurate est...

We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the “global measure formula” for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we ...

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...

in the present work the recrystallization behavior of deep drawing grade al-killed low carbon steel sheets produced by mobarakeh steel plant (msp) has been studied. salt bath isothermal annealing has been applied to cold rolled samples and the resulted microstrucrures have been compared with the microstructure obtained from the box annealing process in msp. it is found that at 635 and 700ºc the...

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands. Streszczenie. W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie now...

In this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of ‘equi-homogeneity’ of a set, which requires a uniformity in the size of local covers at all lengths and at all points We prove that the Assouad and box-counting dimensions coincide for sets that have equal upper and lowe...