A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IX: QUASI-ERGODICITY

DOI10.1142/S0218127408021853zbMath1157.37300MaRDI QIDQ3619048

Leon O. Chua, Jinwook Shin, Valeriy I. Sbitnev, Giovanni Egidio Pazienza, László Orzó

Publication date: 3 April 2009

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

attractorsnonlinear dynamicscellular automataergodicityfractalsBernoulli shiftshiftsquasi-ergodicityshift mapsadditive rulesBinomial seriesconservative rulesbasin tree diagramBernoulli return timeBernoulli velocitycomplex Bernoulli shiftsIsles of EdenRule 105Rule 150Rule 154Rule 45Rule 60Rule 90scale-free phenomenabasin-tree generation formuladissipative ruleshyper Bernoullipermutive rules

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Cellular automata (computational aspects) (68Q80) Dynamical aspects of cellular automata (37B15) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) Dynamical systems over complex numbers (37Fxx)

Related Items (10)

Symbolics dynamics of elementary cellular automata rule 88 ⋮ A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART XII: PERIOD-3, PERIOD-6, AND PERMUTIVE RULES ⋮ Glider Collisions in Hybrid Cellular Automaton with Memory Rule (43,74) ⋮ A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE. PART XIII: BERNOULLI σ_τ-SHIFT RULES ⋮ A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART XIV: MORE BERNOULLI σ_τ-SHIFT RULES ⋮ THE WOLFRAM MACHINE ⋮ Real Linear Automata with a Continuum of Periodic Solutions for Every Period ⋮ A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE. PART X: PERIOD-1 RULES ⋮ A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART XI: PERIOD-2 RULES ⋮ BINARY CHAOS SYNCHRONIZATION IN ELEMENTARY CELLULAR AUTOMATA

Cites Work

• Unnamed Item
• Unnamed Item
• Algebraic properties of cellular automata
• Ergodic properties of certain surjective cellular automata
• The ``magic rule spaces of neural-like elementary cellular automata
• On ergodic one-dimensional cellular automata
• A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part II: Universal Neuron
• A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART VI: FROM TIME-REVERSIBLE ATTRACTORS TO THE ARROW OF TIME
• A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART VII: ISLES OF EDEN
• A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART VIII: MORE ISLES OF EDEN
• Traveling waves and chaotic properties in cellular automata
• A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART III: PREDICTING THE UNPREDICTABLE
• A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART V: FRACTALS EVERYWHERE
• A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IV: FROM BERNOULLI SHIFT TO 1/f SPECTRUM
• Wavelengths distribution of chaotic travelling waves in some cellular automata.

This page was built for publication: A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IX: QUASI-ERGODICITY