scholarly journals Multilayered Complexity Analysis in Architectural Design: Two Measurement Methods Evaluating Self-Similarity and Complexity

2021 ◽  
Vol 5 (4) ◽  
pp. 244
Author(s):  
Wolfgang E. Lorenz ◽  
Matthias Kulcke
Keyword(s):  
Architectural Design ◽  
Gradient Analysis ◽  
Complexity Analysis ◽  
Measurement Methods ◽  
Counting Method ◽  
Color Analysis ◽  
Self Similarity ◽  
Box Counting ◽  
Recent Method ◽  
Box Counting Method

This article contributes to clarifying the questions of whether and how fractal geometry, i.e., some of its main properties, are suitable to characterize architectural designs. This is done in reference to complexity-related aesthetic qualities in architecture, taking advantage of the measurability of one of them; the fractal dimension. Research in this area so far, has focused on 2-dimensional elevation plans. The authors present several methods to be used on a variety of source formats, among them a recent method to analyze pictures taken from buildings, i.e., 2.5-dimensional representations, to discuss the potential that lies within their combination. Color analysis methods will provide further information on the significance of a multilayered production and observation of results in this realm. In this publication results from the box-counting method are combined with a coordinate-based method for analyzing redundancy of proportions and their interrelations as well as the potential to include further layers of comparison are discussed. It presents a new area of box-counting implementation, a methodologically redesigned gradient analysis and its new algorithm as well as the combination of both. This research shows that in future systems it will be crucial to integrate several strategies to measure balanced aesthetic complexity in architecture.

MULTIFRACTAL ANALYSIS OF SCLEROGLUCAN HYDROGELS FOR DRUG DELIVERY

Fractals ◽  
2011 ◽  
Vol 19 (03) ◽  
pp. 339-346 ◽  
Author(s):  
NORA J. FRANÇOIS ◽  
M. PIACQUADIO LOSADA ◽  
MARTA E. DARAIO
Keyword(s):  
Environmental Scanning Electron Microscopy ◽  
Environmental Scanning ◽  
Counting Method ◽  
Self Similarity ◽  
Gel Structure ◽  
Fermentation Time ◽  
Polymeric Networks ◽  
Box Counting ◽  
Multifractal Theory ◽  
Box Counting Method

The non-homogeneity and complexity of micro network distribution of hydrogel matrices prepared with two scleroglucan biopolymers obtained with different fermentation times were analyzed using environmental scanning electron microscopy (ESEM) and dynamic rheology. ESEM images were processed with the tools of multifractal theory using the box-counting method in order to obtain the gels multifractal spectra. Dynamic rheological measurements indicate that both polymeric networks correspond to physical gels that exhibit a solid like behavior. These results suggest the existence of a relationship between the fermentation time used in the polymer production, the degree of self-similarity and the rigidity of the scleroglucan gel structure.

A Modified Box-Counting Method to Estimate the Fractal Dimensions

2011 ◽  
Vol 58-60 ◽  
pp. 1756-1761 ◽  
Author(s):  
Jie Xu ◽  
Giusepe Lacidogna
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
The Self ◽  
Whole Body ◽  
Counting Method ◽  
Border Effect ◽  
Self Similarity ◽  
Box Counting ◽  
Self Similar ◽  
Box Counting Method

A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size. The modified box-counting method (MBCM), proposed in this study, not only eliminate the shortcomings of the TBCM, but also reflects the physical meaning about the self-similar of the fractal. The applications of MBCM shows a good estimation compared with the theoretical ones, which the biggest difference is smaller than 5%.

scholarly journals FRACTAL DIMENSION AND SELF-SIMILARITY IN ASPARAGUS PLUMOSUS

Fractals ◽  
2002 ◽  
Vol 10 (04) ◽  
pp. 429-434 ◽  
Author(s):  
J. R. CASTREJÓN PITA ◽  
A. SARMIENTO GALÁN ◽  
R. CASTREJÓN GARCÍA
Keyword(s):  
Fractal Dimension ◽  
Counting Method ◽  
Self Similarity ◽  
Box Counting ◽  
Box Counting Method

We measure the fractal dimension of an African plant that is widely cultivated as an 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 quantitative way that this species is a fractal.

Optimization Analysis on Urban Transportation Network of Lanzhou

2014 ◽  
Vol 641-642 ◽  
pp. 685-689
Author(s):  
Han Pu ◽  
Cun Rui Ma
Keyword(s):  
Transportation Network ◽  
Urban Transportation ◽  
Main Idea ◽  
Small World ◽  
Counting Method ◽  
Self Similarity ◽  
Optimization Analysis ◽  
Box Counting ◽  
Network Merging ◽  
Box Counting Method

On the basis of analyzing the model of C space network in Lanzhou, the small world characteristics were found. Combine the main idea of box counting method and weighted network merging mechanism, the evolution mechanism was put forward based on the self-similarity of the network, then the urban transportation network of Lanzhou is optimized by this method and optimization results are obtained.

scholarly journals Fractal Branching Pattern in the Pial Vasculature in the Cat

2001 ◽  
Vol 21 (6) ◽  
pp. 741-753 ◽  
Author(s):  
Peter Hermán ◽  
László Kocsis ◽  
Andras Eke
Keyword(s):  
Structural Elements ◽  
Vascular Networks ◽  
Counting Method ◽  
Self Similarity ◽  
Box Counting ◽  
Capacity Dimension ◽  
Structural Details ◽  
Fractal Character ◽  
Box Counting Method ◽  
Generation Rule

Arborization pattern was studied in pial vascular networks by treating them as fractals. Rather than applying elaborate taxonomy assembled from measures from individual vessel segments and bifurcations arranged in their branching order, the authors' approach captured the structural details at once in high-resolution digital images processed for the skeleton of the networks. The pial networks appear random and at the same time having structural elements similar to each other when viewed at different scales—a property known as self-similarity revealed by the geometry of fractals. Fractal (capacity) dimension, Dcap, was calculated to evaluate the network's spatial complexity by the box counting method (BCM) and its variant, the extended counting method (XCM). Box counting method and XCM were subject to numerical testing on ideal fractals of known D. The authors found that precision of these fractal methods depends on the fractal character (branching, nonbranching) of the structure they evaluate. Dcap s (group mean ± SD) for the arterial and venous pial networks in the cat (n = 6) are 1.37 ± 0.04, 1.37 ± 0.02 by XCM, and 1.30 ± 0.04, 1.31 ± 0.03 by BCM, respectively. The arterial and venous systems thus appear to be developed according to the same fractal generation rule in the cat.

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

2021 ◽  
Author(s):  
Nicholas Dudu ◽  
Arturo Rodriguez ◽  
Gael Moran ◽  
Jose Terrazas ◽  
Richard Adansi ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Atmospheric Turbulence ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Counting Method ◽  
Data Set ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Self Similar ◽  
Box Counting Method

Abstract Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

Research on a precise differential box-counting method of eliminating image background

2016 ◽  
Author(s):  
Kexue Lai ◽  
Tao He ◽  
Cancan Li ◽  
Weisong Zhou ◽  
Liangen Yang
Keyword(s):  
Counting Method ◽  
Box Counting ◽  
Box Counting Method

scholarly journals Application of An Exponential Mathematical Law of Cardiac Dynamics In 16 Hours

2021 ◽  
Author(s):  
Javier Oswaldo Rodríguez Velásquez ◽  
Sandra Catalina Correra Herrera ◽  
Yesica Tatiana Beltrán Gómez ◽  
Jorge Gómez Rojas ◽  
Signed Esperanza Prieto Bohórquez ◽  
...  
Keyword(s):  
Kappa Coefficient ◽  
Medical Attention ◽  
Chaotic Attractors ◽  
Counting Method ◽  
Statistical Validation ◽  
Overlapping Grids ◽  
Box Counting ◽  
Cardiac Dynamics ◽  
Box Counting Method ◽  
Time Required

Abstract Introduction and objectives: nonlinear dynamics and fractal geometry have allowed the advent of an exponential mathematical law applicable to diagnose cardiac dynamics in 21 hours, however, it would be beneficial to reduce the time required to diagnose cardiac dynamics with this method in critical scenarios, in order to detect earlier complications that may require medical attention. The objective of this research is to confirm the clinical applicability of the mathematical law in 16 hours, with a comparative study against the Gold Standard. Methods: There were taken 450 electrocardiographic records of healthy patients and with cardiac diseases. A physical-mathematical diagnosis was applied to study cardiac dynamics, which consists of generating cardiac chaotic attractors based on the sequence of heart rate values during 16 hours, which were then measured with two overlapping grids according to the Box-Counting method to quantify the spatial occupation and the fractal dimension of each cardiac dynamic, with its respective statistical validation. Results: The occupation spaces of normal dynamics calculated in 16 hours were compatible with previous parameters established, evidencing the precision of the methodology to differentiate normality from abnormality. Sensitivity and specificity values of 100% were found, as well as a Kappa coefficient of 1. Conclusions: it was possible to establish differences between cardiac dynamics for 16 hours, suggesting that this method could be clinically applicable to analyze and diagnose cardiac dynamics in real time.

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