1. IntroductionCellular automata, o

1. Introduction
Cellular automata, originally developed by von Neuman and Ulam in the 1940’s to model biological systems, are discrete
dynamical systems that are known for their strong modeling and self-organizational properties (for examples of some
modeling properties see [3,5,22–24,26]). Cellular automata are defined on an infinite lattice and can be defined for all
dimensions. In the one-dimensional case the integer lattice Z is used. In the two-dimensional case, Z  Z. An example of
a two-dimensional cellular automata is John Conway’s ever popular ‘‘Game of Life’’1. Probably the most interesting aspect
about cellular automata is that which seems to conflict our physical systems. While physical systems tend to maximal entropy,
even starting with complete disorder, forward evolution of cellular automata can generate highly organized structure.
As with all dynamical systems, it is important and interesting to understand their long term or evolutionary behavior.
Hence it makes sense to develop a classification of a system based on its dynamical behavior. The concept of classifying cellular
automata was initiated by Stephen Wolfram in the early 1980’s, see [25,26]. Through numerous computer simulations,
Wolfram noticed that if an initial configuration (sequence) was chosen at random the probability is high that a cellular
automaton rule will fall within one of four classes.
The examples to follow are referred to by a rule numbering system developed by Wolfram, see [25,27]. In [27], onedimensional
cellular automata are partitioned into four classes depending on their dynamical behavior, see Fig. 1 (Totalistic
Rule 36) for an example of a Wolfram class 1 cellular automaton. Class 1 are the least chaotic, indeed Wolfram labeled these
as automata that evolve to a uniform state. Fig. 2 (Totalistic Rule 24) is an example of a Wolfram class 2 cellular automaton

ผลลัพธ์ (ไทย) 1:

1. IntroductionCellular automata, originally developed by von Neuman and Ulam in the 1940’s to model biological systems, are discretedynamical systems that are known for their strong modeling and self-organizational properties (for examples of somemodeling properties see [3,5,22–24,26]). Cellular automata are defined on an infinite lattice and can be defined for alldimensions. In the one-dimensional case the integer lattice Z is used. In the two-dimensional case, Z  Z. An example ofa two-dimensional cellular automata is John Conway’s ever popular ‘‘Game of Life’’1. Probably the most interesting aspectabout cellular automata is that which seems to conflict our physical systems. While physical systems tend to maximal entropy,even starting with complete disorder, forward evolution of cellular automata can generate highly organized structure.As with all dynamical systems, it is important and interesting to understand their long term or evolutionary behavior.Hence it makes sense to develop a classification of a system based on its dynamical behavior. The concept of classifying cellularautomata was initiated by Stephen Wolfram in the early 1980’s, see [25,26]. Through numerous computer simulations,Wolfram noticed that if an initial configuration (sequence) was chosen at random the probability is high that a cellularautomaton rule will fall within one of four classes.ตัวอย่างตามที่อ้างถึง โดยกฎหมายเลขระบบที่พัฒนา โดย Wolfram ดู [25,27] ใน [27], onedimensionalเซลลูลาร์ออโตมาตาจะแบ่งออกเป็น 4 ชั้นตามลักษณะการทำงาน dynamical ดู Fig. 1 (Totalisticกฎ 36) สำหรับตัวอย่างของการ Wolfram คลาส 1 เซลลูลาร์ออโตมาตานั้น คลาส 1 จะวุ่นวายน้อยที่สุด แท้ Wolfram ป้ายเหล่านี้เป็นออโตมาตา ที่พัฒนาสู่สภาวะสม่ำเสมอ Fig. 2 (Totalistic กฎ 24) เป็นตัวอย่างของการ Wolfram คลาส 2 เซลลูลาร์ออโตมาตา

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