Discrete Systems With Memory

¡ World Scientific Series On Nonlinear Science Series A āĻŦāĻ‡ 75 ¡ World Scientific
āĻ‡-āĻŦā§āĻ•
480
āĻĒā§ƒāĻˇā§āĻ āĻž
āĻ‰āĻĒāĻ¯ā§āĻ•ā§āĻ¤
āĻ°ā§‡āĻŸāĻŋāĻ‚ āĻ“ āĻ°āĻŋāĻ­āĻŋāĻ‰ āĻ¯āĻžāĻšāĻžāĻ‡ āĻ•āĻ°āĻž āĻšā§ŸāĻ¨āĻŋ  āĻ†āĻ°āĻ“ āĻœāĻžāĻ¨ā§āĻ¨

āĻāĻ‡ āĻ‡-āĻŦā§āĻ•ā§‡āĻ° āĻŦāĻŋāĻˇā§Ÿā§‡

Memory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions.It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian: only the actual configuration is taken into account to generate the next one.Generalizing the conventional view on spatially extended discrete dynamical systems evolution by allowing cells (or nodes) to be featured by some trait state computed as a function of its own previous state-values, the transition maps of the classical systems are kept unaltered, so that the effect of memory can be easily traced.The book demonstrates that discrete dynamical systems with memory are not only priceless tools for modeling natural phenomena but unique mathematical and aesthetic objects.

āĻ‡-āĻŦā§āĻ•ā§‡ āĻ°ā§‡āĻŸāĻŋāĻ‚ āĻĻāĻŋāĻ¨

āĻ†āĻĒāĻ¨āĻžāĻ° āĻŽāĻ¤āĻžāĻŽāĻ¤ āĻœāĻžāĻ¨āĻžāĻ¨āĨ¤

āĻĒāĻ āĻ¨ āĻ¤āĻĨā§āĻ¯

āĻ¸ā§āĻŽāĻžāĻ°ā§āĻŸāĻĢā§‹āĻ¨ āĻāĻŦāĻ‚ āĻŸā§āĻ¯āĻžāĻŦāĻ˛ā§‡āĻŸ
Android āĻāĻŦāĻ‚ iPad/iPhone āĻāĻ° āĻœāĻ¨ā§āĻ¯ Google Play āĻŦāĻ‡ āĻ…ā§āĻ¯āĻžāĻĒ āĻ‡āĻ¨āĻ¸ā§āĻŸāĻ˛ āĻ•āĻ°ā§āĻ¨āĨ¤ āĻāĻŸāĻŋ āĻ†āĻĒāĻ¨āĻžāĻ° āĻ…ā§āĻ¯āĻžāĻ•āĻžāĻ‰āĻ¨ā§āĻŸā§‡āĻ° āĻ¸āĻžāĻĨā§‡ āĻ…āĻŸā§‹āĻŽā§‡āĻŸāĻŋāĻ• āĻ¸āĻŋāĻ™ā§āĻ• āĻšā§Ÿ āĻ“ āĻ†āĻĒāĻ¨āĻŋ āĻ…āĻ¨āĻ˛āĻžāĻ‡āĻ¨ āĻŦāĻž āĻ…āĻĢāĻ˛āĻžāĻ‡āĻ¨ āĻ¯āĻžāĻ‡ āĻĨāĻžāĻ•ā§āĻ¨ āĻ¨āĻž āĻ•ā§‡āĻ¨ āĻ†āĻĒāĻ¨āĻžāĻ•ā§‡ āĻĒā§œāĻ¤ā§‡ āĻĻā§‡ā§ŸāĨ¤
āĻ˛ā§āĻ¯āĻžāĻĒāĻŸāĻĒ āĻ“ āĻ•āĻŽā§āĻĒāĻŋāĻ‰āĻŸāĻžāĻ°
Google Play āĻĨā§‡āĻ•ā§‡ āĻ•ā§‡āĻ¨āĻž āĻ…āĻĄāĻŋāĻ“āĻŦā§āĻ• āĻ†āĻĒāĻ¨āĻŋ āĻ•āĻŽā§āĻĒāĻŋāĻ‰āĻŸāĻžāĻ°ā§‡āĻ° āĻ“ā§Ÿā§‡āĻŦ āĻŦā§āĻ°āĻžāĻ‰āĻœāĻžāĻ°ā§‡ āĻļā§āĻ¨āĻ¤ā§‡ āĻĒāĻžāĻ°ā§‡āĻ¨āĨ¤
eReader āĻāĻŦāĻ‚ āĻ…āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯ āĻĄāĻŋāĻ­āĻžāĻ‡āĻ¸
Kobo eReaders-āĻāĻ° āĻŽāĻ¤ā§‹ e-ink āĻĄāĻŋāĻ­āĻžāĻ‡āĻ¸ā§‡ āĻĒāĻĄāĻŧāĻ¤ā§‡, āĻ†āĻĒāĻ¨āĻžāĻ•ā§‡ āĻāĻ•āĻŸāĻŋ āĻĢāĻžāĻ‡āĻ˛ āĻĄāĻžāĻ‰āĻ¨āĻ˛ā§‹āĻĄ āĻ“ āĻ†āĻĒāĻ¨āĻžāĻ° āĻĄāĻŋāĻ­āĻžāĻ‡āĻ¸ā§‡ āĻŸā§āĻ°āĻžāĻ¨ā§āĻ¸āĻĢāĻžāĻ° āĻ•āĻ°āĻ¤ā§‡ āĻšāĻŦā§‡āĨ¤ āĻŦā§āĻ¯āĻŦāĻšāĻžāĻ°āĻ•āĻžāĻ°ā§€āĻ° āĻ‰āĻĻā§āĻĻā§‡āĻļā§āĻ¯ā§‡ āĻ¤ā§ˆāĻ°āĻŋ āĻ¸āĻšāĻžā§ŸāĻ¤āĻž āĻ•ā§‡āĻ¨ā§āĻĻā§āĻ°āĻ¤ā§‡ āĻĻā§‡āĻ“ā§ŸāĻž āĻ¨āĻŋāĻ°ā§āĻĻā§‡āĻļāĻžāĻŦāĻ˛ā§€ āĻ…āĻ¨ā§āĻ¸āĻ°āĻŖ āĻ•āĻ°ā§‡ āĻ¯ā§‡āĻ¸āĻŦ eReader-āĻ āĻĢāĻžāĻ‡āĻ˛ āĻĒāĻĄāĻŧāĻž āĻ¯āĻžāĻŦā§‡ āĻ¸ā§‡āĻ–āĻžāĻ¨ā§‡ āĻŸā§āĻ°āĻžāĻ¨ā§āĻ¸āĻĢāĻžāĻ° āĻ•āĻ°ā§āĻ¨āĨ¤

āĻ¸āĻŋāĻ°āĻŋāĻœ āĻĒāĻĄāĻŧāĻž āĻšāĻžāĻ˛āĻŋā§Ÿā§‡ āĻ¯āĻžāĻ¨

Ramon Alonso-sanz āĻāĻ° āĻĨā§‡āĻ•ā§‡ āĻ†āĻ°ā§‹

āĻāĻ•āĻ‡ āĻ§āĻ°āĻ¨ā§‡āĻ° āĻ‡-āĻŦā§āĻ•