THE DYNAMICS OF FRACTALS

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 415-429 ◽  
Author(s):  
PER BAK ◽  
MAYA PACZUSKI
Keyword(s):  
Long Range ◽  
Critical State ◽  
Temporal Dimension ◽  
Punctuated Equilibria ◽  
Temporal Properties ◽  
Numerical Studies ◽  
Avalanche Dynamics ◽  
Fractal Attractor ◽  
Hurst Exponents ◽  
Simple Models

Fractals are formed by avalanches, driving the system toward a critical state. This critical state is a fractal in d spatial plus one temporal dimension. Long range spatial and temporal properties are described by different cuts in this fractal attractor. We unify the origin of fractals, 1/f noise, Hurst exponents, Levy flights, and punctuated equilibria in terms of avalanche dynamics, and elucidate their relationships through analytical and numerical studies of simple models.

scholarly journals Neuronal long-range temporal correlations and avalanche dynamics are correlated with behavioral scaling laws

2013 ◽  
Vol 110 (9) ◽  
pp. 3585-3590 ◽  
Author(s):  
J. Matias Palva ◽  
Alexander Zhigalov ◽  
Jonni Hirvonen ◽  
Onerva Korhonen ◽  
Klaus Linkenkaer-Hansen ◽  
...  
Keyword(s):  
Long Range ◽  
Scaling Laws ◽  
Temporal Correlations ◽  
Avalanche Dynamics

Critical state in superconducting single-crystallineYBa2Cu3O7foams: Local versus long-range currents

2004 ◽  
Vol 70 (14) ◽  
Author(s):  
E. Bartolomé ◽  
X. Granados ◽  
T. Puig ◽  
X. Obradors ◽  
E. S. Reddy ◽  
...  
Keyword(s):  
Long Range ◽  
Critical State

scholarly journals Self-diffusion in simple models: Systems with long-range jumps

1997 ◽  
Vol 87 (5-6) ◽  
pp. 1131-1144 ◽  
Author(s):  
A. Asselah ◽  
R. Brito ◽  
J. L. Lebowitz
Keyword(s):  
Long Range ◽  
Self Diffusion ◽  
Simple Models

scholarly journals SECOND-ORDER DYNAMICS IN THE COLLECTIVE EVOLUTION OF COUPLED MAPS AND AUTOMATA

1992 ◽  
Vol 06 (29) ◽  
pp. 1835-1841 ◽  
Author(s):  
PHILIPPE-MICHEL BINDER ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Dynamical Systems ◽  
Difference Equations ◽  
Order Parameter ◽  
Second Order ◽  
Many Body ◽  
Order Difference ◽  
Temporal Properties ◽  
Numerical Studies ◽  
Coupled Maps ◽  
Collective States

We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations.

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