Self-similar and fractal nature of Internet traffic

2004 ◽  
Vol 14 (2) ◽  
pp. 119-129 ◽  
Author(s):  
D. Chakraborty ◽  
A. Ashir ◽  
T. Suganuma ◽  
G. Mansfield Keeni ◽  
T. K. Roy ◽  
...  
Keyword(s):  
Internet Traffic ◽  
Fractal Nature ◽  
Self Similar

scholarly journals The fractal nature of nature: power laws, ecological complexity and biodiversity

2002 ◽  
Vol 357 (1421) ◽  
pp. 619-626 ◽  
Author(s):  
James H. Brown ◽  
Vijay K. Gupta ◽  
Bai-Lian Li ◽  
Bruce T. Milne ◽  
Carla Restrepo ◽  
...  
Keyword(s):  
Power Laws ◽  
Biological Processes ◽  
Fractal Nature ◽  
Future Prospects ◽  
Wide Range ◽  
Ecological Complexity ◽  
Self Similar ◽  
Underlying Mechanisms ◽  
Diversity Of Life ◽  
Fundamental Physical

Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes. Power laws describe empirical scaling relationships that are emergent quantitative features of biodiversity. These features are patterns of structure or dynamics that are self–similar or fractal–like over many orders of magnitude. Power laws allow extrapolation and prediction over a wide range of scales. Some appear to be universal, occurring in virtually all taxa of organisms and types of environments. They offer clues to underlying mechanisms that powerfully constrain biodiversity. We describe recent progress and future prospects for understanding the mechanisms that generate these power laws, and for explaining the diversity of species and complexity of ecosystems in terms of fundamental principles of physical and biological science.

FRACTAL ELECTRODEPOSITS: MORPHOLOGY, GROWTH DYNAMICS AND DIFFUSION-LIMITED RESPONSE FUNCTIONS

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 439-450 ◽  
Author(s):  
PEDRO PABLO TRIGUEROS ◽  
JORDI MACH ◽  
JOSEP CLARET ◽  
FRANCESC MAS ◽  
FRANCESC SAGUÉS
Keyword(s):  
Growth Dynamics ◽  
Response Functions ◽  
Fractal Nature ◽  
Laplacian Growth ◽  
Applied Potential ◽  
Diffusion Limited ◽  
Electrochemical Processes ◽  
Self Similar ◽  
And Diffusion

Fractal characterization of zinc electrodeposits obtained in a quasi two-dimensional film cell under suitable applied potential and zinc sulphate concentrations is reported. Our results show that these deposits are formed according to a Laplacian growth mode, and moreover, their self-similar fractal nature allows the generalization of the Cottrell law for diffusion-limited electrochemical processes occurring on these surfaces.

scholarly journals Spatial Variation of the Land Snail Brephulopsis Cylindrica (Gastropoda, Pulmonata, Enidae): A Fractal Approach

2014 ◽  
Vol 48 (5) ◽  
pp. 433-440
Author(s):  
S. S. Kramarenko ◽  
I. V. Dovgal
Keyword(s):  
Fractal Dimension ◽  
Spatial Variability ◽  
Spatial Variation ◽  
Land Snail ◽  
Morphological Characters ◽  
The Self ◽  
Fractal Nature ◽  
Fractal Approach ◽  
Self Similar ◽  
Similar Elements

Abstract Spatial Variation of the Land Snail Brephulopsis cylindrica (Gastropoda, Pulmonata, Enidae): a Fractal Approach. Kramarenko, S. S., Dovgal, I. V. - Th e results of investigations of intrapopulation patterns in the land snail Brephulopsis cylindrica (Menke, 1828) variation are discussed in the article. Th e self-similar intrapopulational groups (demes) with sets of random (chaotic) and ranked (clinal) patterns of morphological characters were observed. It is argued that the self-similar elements lead to the formation of spatial variability patterns with distinct fractal nature. Thus the relative roles both of the random and the regular components can be detected for separate characters according to the degrees of nearness or remoteness of fractal dimension to 2.0.

scholarly journals Mathematics in Internet Traffic Data Analysis

2011 ◽  
pp. 59-67
Author(s):  
Sasmita Acharya ◽  
Sasmita Mishra ◽  
S.N. Mishra
Keyword(s):  
Spatial Scales ◽  
Internet Traffic ◽  
The Self ◽  
Traffic Data ◽  
Similar Nature ◽  
Main Research ◽  
Wide Range ◽  
Extreme Variability ◽  
Fractal Characteristics ◽  
Self Similar

The Internet traffic data have been found to possess extreme variability and bursty structures in a wide range of time-scales, so that there is no definite duration of busy or silent periods. But there is a self-similarity for which it is possible to characterize the data. The self-similar nature was first proposed by Leland et a1 [l] and subsequently established by others in a flood of research works on the subject [2]-[5]. It was then a new concept against the long believed idea of Poisson traffic. The traditional Poison model, a short ranged process, assumed the variation of data flow to be finite but the observations on Internet traffic proved otherwise. It is this large variance that leads to the self-similar nature of the data almost at all scales of resolution. Such a feature is always associated with a fractal structure of the data. The fractal characteristics can exist both in temporal and spatial scales. This was indicated by Willinger and Paxson [6], as due to the extreme variability and long range dependence in the process. Presently, one of the main research interests in the field of Internet traffic is that of prediction of data which will help a network manager to render a satisfactory quality of service. Before preparing a model of prediction, one of the important tasks is to determine its statistics. Any model to predict the future values will have to preserve these characteristics.

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