scholarly journals Fractal Features of Proto-Plant’s Origin and their Possible Consequences

2016 ◽  
Author(s):  
V.V. Galitskii
Keyword(s):  
Seed Germination ◽  
Slow Growth ◽  
Higher Plants ◽  
Counting Method ◽  
Photosynthetic System ◽  
Anatomical Features ◽  
Fractal Parameter ◽  
Box Counting ◽  
Fractal Properties ◽  
Box Counting Method

AbstractThe extension of the sectional model of the spruce crown’s dynamics into diapason (0, 1) of the fractal parameter μ has demonstrated the existence of green biomass on branches of three orders in form of photosynthesizing (green) points. We investigated the growth of point sets on an interval as a model of the origin of proto-plants, which are formed due to endosymbiosis of cyanobacteria and protists. The fractal properties of the sets of evenly placed points and group sets were studied using the box-counting method. For the group sets, the character of dependence μ on the growing total number of points changes radically differently depending on whether the number of the points per group or the number of groups was fixed. As the host does not have the initial infrastructure needed for an increase in cyanobacteria per group, the first path is implemented and μ decreases from 1 to 0.25 when groups consist of two points per group. If and when the host develops necessary anatomical features (infrastructure), the second pathway is realized and μ grows to 1. The combined trajectory of μ initially demonstrates a slow growth of the size of the photosynthetic system and then an exponential growth after the development of the host’s infrastructure. Similar fractal peculiarity also characterizes trees and is an innate property of plants. Assumptions on the morphological recapitulation of proto-plant in higher plants’ ontogenesis (embryogenesis and seed germination) and also a possibility to fix the number of cyanobacteria per group are discussed.

scholarly journals Fractal Properties of CdTe Quantum Dots Dendrites-=SUP=-*-=/SUP=-

2020 ◽  
Vol 128 (8) ◽  
pp. 1190
Author(s):  
O.M. Kushchenko ◽  
S.S. Rudyi ◽  
L.N. Borodina ◽  
S.A. Cherevkov ◽  
Yu.V. Rozhdestvensky
Keyword(s):  
Quantum Dots ◽  
Fractal Dimension ◽  
Spectral Characteristics ◽  
Dendritic Structure ◽  
Minkowski Dimension ◽  
Counting Method ◽  
Box Counting ◽  
Fractal Properties ◽  
Luminescence Peak ◽  
Box Counting Method

Here we present the analyses of fractal properties of CdTe dendrites. The spectral characteristics of dendrites obtained at different acids of the initial solution were investigated. We demonstrate the displacement of the local luminescence peak depended on the branches of the dendritic structure. The fractal dimension has been calculated by the box-counting method. We obtained the correlation between the local peak of luminescence and the Minkowski dimension.

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.

scholarly journals Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Youping Fan ◽  
Dai Zhang ◽  
Jingjiao Li
Keyword(s):  
Fractal Dimension ◽  
Tree Growth ◽  
Fractal Dimensions ◽  
Moisture Level ◽  
Growth Time ◽  
Counting Method ◽  
Box Counting ◽  
Electrical Trees ◽  
Box Counting Method ◽  
Electrical Treeing

The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.

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.

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