Dynamics of a Vicsek fractal: The boundary effect and the interplay among the local symmetry, the self-similarity, and the structure of the fractal

1994 ◽  
Vol 50 (2) ◽  
pp. 897-906 ◽  
Author(s):  
C. S. Jayanthi ◽  
S. Y. Wu
Keyword(s):  
Boundary Effect ◽  
Local Symmetry ◽  
The Self ◽  
Self Similarity

scholarly journals CAN AGN FEEDBACK BREAK THE SELF-SIMILARITY OF GALAXIES, GROUPS, AND CLUSTERS?

2014 ◽  
Vol 783 (1) ◽  
pp. L10 ◽  
Author(s):  
M. Gaspari ◽  
F. Brighenti ◽  
P. Temi ◽  
S. Ettori
Keyword(s):  
The Self ◽  
Self Similarity

scholarly journals On the self-similarity of diffracting gaseous detonations and the critical channel width problem

2021 ◽  
Vol 33 (6) ◽  
pp. 066106
Author(s):  
M. I. Radulescu ◽  
R. Mével ◽  
Q. Xiao ◽  
S. Gallier
Keyword(s):  
The Self ◽  
Channel Width ◽  
Self Similarity ◽  
Gaseous Detonations

Judged Beauty of Fractal Symmetries

2021 ◽  
pp. 027623742199469
Author(s):  
Jay Friedenberg ◽  
Preston Martin ◽  
Naomi Uy ◽  
Mackenzie Kvapil
Keyword(s):  
Local Symmetry ◽  
Self Similarity ◽  
Vertical Orientation ◽  
Degree Of Similarity ◽  
Different Levels

Fractals are patterns that show self-similarity at different levels of scale. Typically they appear in nature and this degree of similarity is approximate or statistical. However, artificial or exact fractals have also been studied and the advantage of these stimuli is the ability to more carefully control the relationships that occur across various hierarchies. In two experiments we studied the perceived beauty of a novel class of exact visual fractal in which we introduced reflection, rotation, translation, and random symmetries that repeated at a local and global levels. Rotation and reflection were consistently preferred to translation and randomness. Only reflected patterns were preferred at a vertical orientation. For all other symmetries there was no difference in preference between vertical and horizontal. In a second experiment we progressively eliminated the salience of local symmetry through opaque shading . Perceived beauty decreased with an increase in shading . For these patterns greater discriminability of their fractal quality makes them more aesthetically appealing.

scholarly journals A Community-Structure-Based Method for Estimating the Fractal Dimension, and its Application to Water Networks for the Assessment of Vulnerability to Disasters

2021 ◽  
Vol 35 (4) ◽  
pp. 1197-1210
Author(s):  
C. Giudicianni ◽  
A. Di Nardo ◽  
R. Greco ◽  
A. Scala
Keyword(s):  
Fractal Dimension ◽  
Community Structure ◽  
Distribution Systems ◽  
Water Distribution ◽  
Scaling Law ◽  
Vulnerability Index ◽  
The Self ◽  
Node Degree ◽  
Specific Response ◽  
Self Similarity

AbstractMost real-world networks, from the World-Wide-Web to biological systems, are known to have common structural properties. A remarkable point is fractality, which suggests the self-similarity across scales of the network structure of these complex systems. Managing the computational complexity for detecting the self-similarity of big-sized systems represents a crucial problem. In this paper, a novel algorithm for revealing the fractality, that exploits the community structure principle, is proposed and then applied to several water distribution systems (WDSs) of different size, unveiling a self-similar feature of their layouts. A scaling-law relationship, linking the number of clusters necessary for covering the network and their average size is defined, the exponent of which represents the fractal dimension. The self-similarity is then investigated as a proxy of recurrent and specific response to multiple random pipe failures – like during natural disasters – pointing out a specific global vulnerability for each WDS. A novel vulnerability index, called Cut-Vulnerability is introduced as the ratio between the fractal dimension and the average node degree, and its relationships with the number of randomly removed pipes necessary to disconnect the network and with some topological metrics are investigated. The analysis shows the effectiveness of the novel index in describing the global vulnerability of WDSs.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 349-361 ◽  
Author(s):  
BÜNYAMIN DEMÍR ◽  
ALI DENÍZ ◽  
ŞAHIN KOÇAK ◽  
A. ERSIN ÜREYEN
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Complex Dimensions ◽  
Tubular Neighborhoods ◽  
Self Similar ◽  
Tube Formulas

Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph self-similarity of Mauldin-Williams within this framework of Lapidus-Pearse. Extending the notion of complex dimensions to the graph-directed fractals we compute the volumes of tubular neighborhoods of their associated tilings and give a simplified and pointwise proof of a version of Lapidus-Pearse formula, which can be applied to both self-similar and graph-directed fractals.

scholarly journals The Self-Similarity of Shear-dominated Viscous Stirring

2007 ◽  
Vol 133 (5) ◽  
pp. 2389-2392 ◽  
Author(s):  
Benjamin F. Collins ◽  
Hilke E. Schlichting ◽  
Re'em Sari
Keyword(s):  
The Self ◽  
Self Similarity
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