Lacunarity and Period-doubling
نویسندگان
چکیده
We show that the deviation from power laws of the scaling of chaotic measures such as Lyapunov exponents and topological entropy is periodic in the logarithm of the distance from the accumulation of period doubling. Moreover, this periodic function is asymptotically universal for each measure (for functions in the appropriate universality class). This is related to the concept of lacunarity known to exist for scaling functions describing the mass distribution of self-similar fractal sets.
منابع مشابه
Lacunarity Analysis: A Promising Method for the Automated Assessment of Melanocytic Naevi and Melanoma
The early diagnosis of melanoma is critical to achieving reduced mortality and increased survival. Although clinical examination is currently the method of choice for melanocytic lesion assessment, there is a growing interest among clinicians regarding the potential diagnostic utility of computerised image analysis. Recognising that there exist significant shortcomings in currently available al...
متن کاملTexture Classification Using Fractal Dimension and Lacunarity
The fractal features including fractal dimension (FD) and lacunarity measures are often used as indicators of texture. Several FD and lacunarity estimation methods leading to different results have been proposed in the literature. This paper is devoted mainly to show the need to combine the lacunarity with fractal dimension for the discrimination between different textures and especially to che...
متن کاملInfluence of image resolution and evaluation algorithm on estimates of the lacunarity of porous media.
In recent years, experience has demonstrated that the classical fractal dimensions are not sufficient to describe uniquely the interstitial geometry of porous media. At least one additional index or dimension is necessary. Lacunarity, a measure of the degree to which a data set is translationally invariant, is a possible candidate. Unfortunately, several approaches exist to evaluate it on the b...
متن کاملEvaluating Mandibular Cortical Index Quantitatively
OBJECTIVES The aim was to assess whether Fractal Dimension and Lacunarity analysis can discriminate patients having different mandibular cortical shape. METHODS Panoramic radiographs of 52 patients were evaluated for mandibular cortical index. Weighted Kappa between the observations were varying between 0.718-0.805. These radiographs were scanned and converted to binary images. Fractal Dimens...
متن کاملLacunarity analysis of raster datasets and 1D, 2D, and 3D point patterns
Spatial scale plays an important role in many fields. As a scale-dependent measure for spatial heterogeneity, lacunarity describes the distribution of gaps within a set at multiple scales. In Earth science, environmental science, and ecology, lacunarity has been increasingly used for multiscale modeling of spatial patterns. This paper presents the development and implementation of a geographic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012