Number-conserving cellular automaton rules
نویسندگان
چکیده
A necessary and sufficient condition for a one-dimensional q-state n-input cellular automaton rule to be number-conserving is established. Two different forms of simpler and more visual representations of these rules are given, and their flow diagrams are determined. Various examples are presented and applications to car traffic are indicated. Two nontrivial three-state threeinput self-conjugate rules have been found. They can be used to model the dynamics of random walkers.
منابع مشابه
Eventually Number-Conserving Cellular Automata
We present a preliminary study of a new class of two-input cellular automaton rules called eventually number-conserving rules characterized by the property of evolving after a finite number of time steps to states whose number of active sites remains constant. Viewed as models of systems of interacting particles, these rules obey a kind of Darwinian principle by either annihilating unnecessary ...
متن کاملEmbedding a Logically Universal Model and a Self-Reproducing Model into Number-Conserving Cellular Automata
A number-conserving cellular automaton (NCCA) is a cellular automaton (CA) such that all states of cells are represented by integers and the total number of its configuration is conserved throughout its computing process. It can be thought as a kind of modelization of the physical conservation law of mass or energy. Although NCCAs with simple rules are studied widely, it is quite difficult to d...
متن کاملD ec 1 99 7 Cellular automaton rules conserving the number of active sites
This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interactin...
متن کاملA ug 1 99 8 Cellular automaton rules conserving the number of active sites
This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interactin...
متن کاملMotion representation of one - dimensional cellular automaton rules
Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears in the discrete version of the continuity equation, completed by the discrete analogue of the source term. This new representation is general , but not uniqu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Fundam. Inform.
دوره 52 شماره
صفحات -
تاریخ انتشار 2002