Resistance dimension, random walk dimension and fractal dimension

1993 ◽  
Vol 6 (4) ◽  
pp. 635-652 ◽  
Author(s):  
Xian Yin Zhou
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Walk Dimension

A compass without a map: tortuosity and orientation of eastern painted turtles (Chrysemys picta picta) released in unfamiliar territory

2006 ◽  
Vol 84 (8) ◽  
pp. 1129-1137 ◽  
Author(s):  
I.R. Caldwell ◽  
V.O. Nams
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Spatial Scales ◽  
Chrysemys Picta ◽  
Reference Stimulus ◽  
Correlated Random Walk ◽  
Specific Mechanism ◽  
Minimal Time ◽  
Painted Turtles

Orientation mechanisms allow animals to spend minimal time in hostile areas while reaching needed resources. Identification of the specific mechanism used by an animal can be difficult, but examining an animal's path in familiar and unfamiliar areas can provide clues to the type of mechanism in use. Semiaquatic turtles are known to use a homing mechanism in familiar territory to locate their home lake while on land, but little is known about their ability to locate habitat in unfamiliar territory. We tested the tortuosity and orientation of 60 eastern painted turtles ( Chrysemys picta picta (Schneider, 1783)). We released turtles at 20 release points located at five distances and in two directions from two unfamiliar lakes. Turtle trails were quite straight (fractal dimension between 1.1 and 1.025) but were not oriented towards water from any distance (V-test; u < 0.72; P > 0.1). Turtles maintained their initially chosen direction but either could not detect water or were not motivated to reach it. Furthermore, paths were straighter at larger spatial scales than at smaller spatial scales, which could not have occurred if the turtles had been using a correlated random walk. Turtles must therefore be using a reference stimulus for navigation even in unfamiliar areas.

scholarly journals Differences in fractal patterns and characteristic periodicities between word salads and normal sentences: Interference of meaning and sound

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0247133
Author(s):  
Jun Shimizu ◽  
Hiromi Kuwata ◽  
Kazuo Kuwata
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Long Range ◽  
Mental State ◽  
Fractal Dimensions ◽  
Social Robots ◽  
Fractal Patterns

Fractal dimensions and characteristic periodicities were evaluated in normal sentences, computer-generated word salads, and word salads from schizophrenia patients, in both Japanese and English, using the random walk patterns of vowels.　In normal sentences, the walking curves were smooth with gentle undulations, whereas computer-generated word salads were rugged with mechanical repetitions, and word salads from patients with schizophrenia were unreasonably winding with meaningless repetitive patterns or even artistic cohesion. These tendencies were similar in both languages. Fractal dimensions between normal sentences and word salads of schizophrenia were significantly different in Japanese [1.19 ± 0.09 (n = 90) and 1.15 ± 0.08 (n = 45), respectively] and English [1.20 ± 0.08 (n = 91), and 1.16 ± 0.08 (n = 42)] (p < 0.05 for both). Differences in long-range (>10) periodicities between normal sentences and word salads from schizophrenia patients were predominantly observed at 25.6 (p < 0.01) in Japanese and 10.7 (p < 0.01) in English. The differences in fractal dimension and characteristic periodicities of relatively long-range (>10) presented here are sensitive to discriminate between schizophrenia and healthy mental state, and could be implemented in social robots to assess the mental state of people in care.

Schramm–Loewner evolution of the accessible perimeter of isoheight lines of correlated landscapes

2018 ◽  
Vol 29 (01) ◽  
pp. 1850008 ◽  
Author(s):  
N. Posé ◽  
K. J. Schrenk ◽  
N. A. M. Araújo ◽  
H. J. Herrmann
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Long Range ◽  
Hurst Exponent ◽  
Diffusion Constant ◽  
Strongly Correlated ◽  
Loewner Evolution ◽  
Positive Formula ◽  
Practical Implications ◽  
Negative Formula

Real landscapes exhibit long-range height–height correlations, which are quantified by the Hurst exponent [Formula: see text]. We give evidence that for negative [Formula: see text], in spite of the long-range nature of correlations, the statistics of the accessible perimeter of isoheight lines is compatible with Schramm–Loewner evolution curves and therefore can be mapped to random walks, their fractal dimension determining the diffusion constant. Analytic results are recovered for [Formula: see text] and [Formula: see text] and a conjecture is proposed for the values in between. By contrast, for positive [Formula: see text], we find that the random walk is not Markovian but strongly correlated in time. Theoretical and practical implications are discussed.

RANDOM WALK IN SHORTCUT MODELS

2008 ◽  
Vol 22 (10) ◽  
pp. 727-733 ◽  
Author(s):  
O. SHANKER
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Drift Velocity ◽  
System Size ◽  
Random Walk Process ◽  
Range Analysis ◽  
Sharp Transition ◽  
Rescaled Range ◽  
Rescaled Range Analysis

Earlier studies of a parametrized class of models whose fractal dimension transitions from one to two indicated that the transition occurs infinitely sharply at the parameter value p=0, as the system size increases to infinity. We study a random walk process which is sensitive to dimension, and we find the same sharp transition at p=0. We use the tool of rescaled range analysis to analyze the drift velocity of the random walk process.

Differential Fractal Dimension of Random Walk and Its Applications to Physical Systems

1982 ◽  
Vol 51 (9) ◽  
pp. 3057-3064 ◽  
Author(s):  
Hideki Takayasu
Keyword(s):  
Fractal Dimension ◽  
Random Walk ◽  
Physical Systems

Monte Carlo simulations of anomalous relaxation in a-Si — random walk in spaces of fractal dimension —

1993 ◽  
Vol 164-166 ◽  
pp. 301-304 ◽  
Author(s):  
S. Fujiwara ◽  
S. Gomi ◽  
K. Morigaki ◽  
F. Yonezawa
Keyword(s):  
Monte Carlo ◽  
Fractal Dimension ◽  
Random Walk ◽  
Monte Carlo Simulations ◽  
Anomalous Relaxation

Determination of the random-walk dimension of fractals by means of NMR

1985 ◽  
Vol 32 (9) ◽  
pp. 6066-6066 ◽  
Author(s):  
Jayanth R. Banavar ◽  
Max Lipsicas ◽  
Jorge F. Willemsen
Keyword(s):  
Random Walk ◽  
Walk Dimension

ON THE IMPACT OF THE BOUNDARY ON DYNAMICS: ANTI-PERSISTENCE IN THE CASE OF THE HKD EXCHANGE RATE CORRIDOR

2015 ◽  
Vol 10 (01) ◽  
pp. 1550006 ◽  
Author(s):  
HONG BEN YEE
Keyword(s):  
Fractal Dimension ◽  
Exchange Rate ◽  
Random Walk ◽  
Hurst Exponent ◽  
Lower Boundary ◽  
The Other ◽  
Rate Process ◽  
Rescaled Range ◽  
The Difference ◽  
The Impact

This paper studies the features of the USD/HKD exchange rate process by assessing the conformity of its dynamics to that of a random walk. This is not a trivial task since we consider the period within which the rate is confined to a specified corridor. This is achieved via analysis of its fractal dimension by means of the Hurst exponent as estimated using the rescaled range method. The conformity can be quantified by the difference between the estimated Hurst exponent and the random walk Hurst exponent of ½. At least two distinct Hurst exponents are identified, one corresponding to a random walk while the other, to an anti-persistent process. Partitioning the rate in state space associates the anti-persistence with proximity to the lower boundary of the corridor so the rate can be modeled using a random walk when sufficiently distant from the boundary.

scholarly journals Fractal Dimension, Walk Dimension and Conductivity Exponent of Karst Networks around Tulum

2016 ◽  
Vol 4 ◽  
Author(s):  
Martin Hendrick ◽  
Philippe Renard
Keyword(s):  
Fractal Dimension ◽  
Walk Dimension
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