Langton, C. Self-reproduction in cellular automata. Physica 10D (1984), 135--144.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a copy of itself from instructions on a tape. Subsequent research reported simpler self replicating structures. Codd produced a sheathed loop structure embedded in an 8 state CA [4] Langton made further reductions and described an 8 state, 86 component, sheathedloop self replicating structure [9]. Recently, even simpler, non trivial self replicating structures have been shown to exist [14] In each of the above and related studies, automata rules were manually designed, and to our knowledge no research has been reported where such rules have been generated automatically. However, in other ....

....would allow the seed structure to produce copies of itself. We distinguish between trivial and non trivial selfreplication by insisting that the structure actively directs the construction of o#spring, as opposed to trivial cases where all component automata simultaneously split to form two copies [9]. The duration or period T of each EA simulation was chosen to be T = 10 time steps because given the small size of the seed structures, it was assumed that if any self replicating processes emerged, it would be during these early time steps. 3.3 Fitness functions Designing a fitness function to ....

C. Langton, Self-Reproduction in Cellular Automata, Physica D, 10, pp. 135--144, 1984.

....models of self replication. Self replicating machines are also related to selfassembling machines and universal constructors. 2. 1 Self Replicating Cellular Automata Since von Neumann s pioneering work [19] after a hiatus, research in self replicating cellular automata is now flourishing [7], 13] 15] 17] 18] Most of this work has involved two dimensional cellular automata. A two dimensional grid of cells forms a discrete space, which is infinite and unbounded in the abstract, but is necessarily finite in a computer implementation. The cells are (usually identical) finite ....

....the red blue bonding angle above 24 or below its current value of # 256 radians. Since there is selection (for rapid replication) JohnnyVon supports a limited degree of evolution: there is inheritance, mutation, and selection. Cellular automata can also support self replication [6] [7], 13] 17] 19] evolution [2] 6] 13] 14] 16] 19] and spontaneous generation of self replication without seeding [2] 6] The novelty in JohnnyVon is that these three features appear in a computer simulation that includes continuous space and virtual physics. We believe that this is ....

Langton, C.G. (1984). Self-reproduction in cellular automata. Physica D, 10, 134144.

....reference a local neighbourhood around the focal cell. The transition rule can be shared ( uniform CAs) or di erent for every cell ( non uniform CAs) CAs change cell states using the mechanism of induction. CAs have been used in a wide range of scienti c research topics such as self replication[Lan84], dynamics of complex systems[Wol83,WL92] etc. More complex computational models have been proposed that exhibit both lineage and interaction. An example particularly well suited in the scope of this paper are Cell Systems , which describe development of planar multi cellular shapes ....

C. G. Langton. Self-reproduction in cellular automata. Physica D, 10(12) :135-144, 1984.

....Work JohnnyVon is related to research in self replicating automata, mobile automata, and physical models of self replication. 2. 1 Self Replicating Cellular Automata Since von Neumann s pioneering work [10] after a hiatus, research in self replicating cellular automata is now flourishing [2], 5] 7] 8] 9] Most of this work has involved two dimensional cellular automata. A two dimensional grid of cells forms a discrete space, which is infinite and unbounded in the abstract, but is necessarily finite in a computer implementation. The cells are (usually identical) finite state ....

....or decreased by adjusting the red blue bonding angle above or below its current value of 256 radians. Since there is selection (for rapid replication) JohnnyVon fully supports evolution: there is inheritance, mutation, and selection. Cellular automata can also support self replication [2], 5] 8] 10] evolution [6] and spontaneous generation of life from non life [1] The novelty in JohnnyVon is that these three features appear in a computer simulation that includes continuous space and virtual physics. We believe that this is an important step towards building ....

Langton, C.G. (1984). Self-reproduction in cellular automata. Physica D, 10, 134144.

....application. This automaton, unfortunately handicapped by its great complexity, was the starting point for much of the further research in the field [2,3,4] The second major event in the study of self replicating CAs is Christopher Langton s development of the automaton known as Langton s loop [5], an automaton where the features of universal construction and universal computation were sacrificed for the sake of simplicity. The result is a small automaton capable exclusively of self replication, extensively used and ameliorated by Langton s successors [6,7] The motivations behind the ....

C. G. Langton. "Self-Reproduction in Cellular Automata". Physica 10D, 1984, pp. 135144.

....dimensional models. One dimensional cellular automata have been extensively studied in the past and generated lots of interesting results [26, 27] Two dimensional cellular automata have also been studied a lot, and are the primary research vehicle for self replication studies in artificial life [3, 15, 5, 19]. Trend was designed to support two dimensional cellular automata programming, thus we focus mainly on 2 D cellular automata models in this article, although 1 D cellular automata can also be simulated with Trend. Each cell in a cellular automata space can be in one of # possible states specified ....

....necessary to write cellular automata rules this way, Trend does have the capability to easily adopt such a table into its rules, if necessary. Therefore, old models can be run in Trend without much modification. The following Trend program implements the well known, Langton s self replicating loop [15], using tables. The transition function domain values, each of them consists of the center, north, east, south and west neighbor values of the von Neumann neighborhood, are listed in the array domain[ Their corresponding next state values are listed in the array next[ This translated rule set ....

[Article contains additional citation context not shown here]

Christopher G. Langton. Self-reproduction in cellular automata. Physica D, 10:135--144, 1984.

....in Table 1. Note that in a strict sense, some of the examples could fit in more than one classification. Table 2 gives an idea of the complexity and interrelation of the systems presented. Level Examples of research done in this level Cellular . Self reproducing cellular automata [4] [5][6] Systolic and wavefront arrays [7] 8] Embryonics [9] 10] Organ . Neural networks [11] 12] Artificial brains [13] 14] Evolvable hardware [15] 16] 17] Design of sensors and actuators [18] 19] System . Artificial limbs [20] Micro machines [21] Hardwired ....

C. Langton, "Self-reproduction in Cellular Automata", Physica 10D, pp.135-144, 1984

....are equivalent to the computing machine, described by Turing (1936) Unfortunately, the capital work of von Neumann [2] was not finished because of his death in 1957. This classical work, however, finds many admirers and imitators, especially in the Sixties and the Seventies, as well as nowadays [6], 7] A matter of special interest in von Neumann s work is his definition of the term non trivial reproduction . According to his understanding, to be non trivially reproducing itself a unit should be simultaneously a universal computer and an universal constructor over a set of conditions. ....

....not been considered of any particular interest, as they lead only to replications. Many researchers do not even consider it necessary to pay any special attention to this fact , thinking it is obvious. Such an opinion is so widely spread, as to, for example, Chris Langton states the following in [6]: Any reproductive process going on here resides entirely in the transition rules and not in the configuration itself. As for the second part of this statement (that the replication is independent of the initial configuration) we can only agree with it, but the conclusion for the transition ....

Langton, Christopher, "Self-Reproduction in Cellular Automata", Physica D 10 (1984), 135--144.

....computation techniques rely upon sexual reproduction, motivated the introduction of such a feature also in the context of Enact. Although a number of cellular automata exhibiting the ability of self reproduction have been discovered for instance, von Neumann 1966] Codd 1968] Banks 1971] [Langton 1984] and [Byl 1989] no cellular automaton embedding a form of sexual reproduction has apparently been reported, other than the one in this thesis. The closest reference in the literature seems to be [Vitanyi 1973] where an abstract discussion is carried out on how to extend the cellular automaton ....

....renders it completely impractical for present purposes, and, in fact, neither of them have ever been implemented. On the other hand, if one wishes to create self reproducing automata it is also important to prevent them from exhibiting a trivial self reproduction. In this respect the point made in [Langton 1984] is relevant. A two state cellular automaton that performs addition modulo 2 described therein exhibits self reproduction, but is overly trivial since it can be fully described at the level of the automaton s underlying physics. That is, its self reproduction cannot be described in terms of ....

[Article contains additional citation context not shown here]

Christopher G. Langton. Self-reproduction in cellular automata. Physica D, 10:134--144, 1984.

....determinism governing von Neumann s machines as well as their lack of fault tolerance, they are not good models of living beings. Moreover, von Neumann left open the question of determining the minimal logical organization necessary for a system to exhibit self reproduction properties. Langton [2,3] showed that self reproduction is not necessarily a particular case of universal constructive capabilities. Other works aimed to improve the results of von Neumann. Codd [1] reduced the number of cell states of the transition rule, but that resulted in an increase of the structural complexity of ....

....W 1 , W 2 , and W 4 of the writing loop area, corresponding to the rightward, upward, and downward motions of the writing head. 10 The Construction The construction can be divided in several phases, each of which is characterized by one of the following groups of constructor states: 0,1] [2,3], 4,5,6] 7,8,9] 10,11] 12] Note that I consider as phase transitions only those state transitions that entail a cabling change in an area of the constructor different from the state control area. In the constructor described in the file tape.evn on Alife Online, the six phases of the ....

[Article contains additional citation context not shown here]

Langton, C. G. (1984). Self--reproduction in cellular automata. Physica 10D, 135--144.

.... groups as follows 1 : 1) Implementation of universal constructors based on von Neumann s self reproducing automaton, studied in 50s 70s (von Neumann 1966; Codd 1968; Vit anyi 1973; Pesavento 1995) 2) Search for a minimal system capable of non trivial self replication, studied in 80s 90s (Langton 1984; Byl 1989; Reggia et al. 1993; Sipper 1994; Morita Imai 1996b) 1 See also (Sayama 1998a, Chap.3) and (Sipper 1998) 3) Addition of other computational capabilities to selfreplicators, studied in 90s present (Tempesti 1995; Perrier, Sipper, Zahnd 1996; Chou Reggia 1998) 4) Realization ....

....of their ability to do more complicated things) is attainable using CA is an open question originally posed by von Neumann at the beginning of this area (von Neumann 1966; Marchal 1998) which still has been unsolved. One of the reasons for this is that the idea of Langton s self replicating loop (Langton 1984) that has formed the basis for many succeeding studies requires a simple, square (or rectangular) shape of organisms to enable their replication. To remove this restriction, it is necessary to employ a model much more exible in terms of the shape of self replicating organisms. The work ....

[Article contains additional citation context not shown here]

Langton, C. G. 1984. Self-reproduction in cellular automata.

....Evolution I now wish to return to issues of reproduction in the specific context of evolution. In this section I will concentrate on a number of these issues in turn. 3. 1 Trivial versus Non Trivial Reproduction Notice that in much of the recent artificial life work with self reproduction (e.g. [4]) the distinction between trivial and non trivial self reproduction is perceived to be a distinction on the implicit explicit axis. 2 However, from an evolutionary point of view, the limited indefinite heredity axis is clearly the most relevant. Indeed, this is exactly what von Neumann himself ....

Langton, C.G.: Self-reproduction in cellular automata. Physica D (1984) 135--144

....the state of its nearest neighbours. There is a finite (usually small) number of possible states for a cell. The transition from one state to the next at discrete time steps in all the cells is what determines the array s behaviour and applications. CAs have been used for studying selfreproduction [8], and modelling of dynamic complex systems [9,10] Systolic Arrays. In systolic arrays the processing elements are designed to match a particular algorithm. Systolic means that synchronous pipelined computations take place along all dimensions of the array and result in very high computational ....

Langton C.: "Self-reproduction in Cellular Automata", Physica 10D, 1984, pp.135-144

....to a computation problem, which means that no machinery beyond ordinary computation theory is required by selfreproduction . But, if computation universality is a sufficient condition for self reproduction, it is not a necessary one, as it is shown by the well known example of Langton [45]. It is a 2 dimensional cellular automaton, with few states, a simple non trivial configuration c 0 of which (a loop of 15x Gamma cells, 10y Gamma cells, for tens of thousands for von Neumann or Codd : is capable of constructing itself periodically, or which appears periodically in the ....

Langton C. Self-Reproduction in Cellular Automata. Physica, Vol. no. 100: 135--144, 1984.

No context found.

Langton, C. Self-reproduction in cellular automata. Physica 10D (1984), 135--144.

No context found.

C.G. Langton. Self-reproduction in cellular automata. Physica 10D, pages 135--144,

No context found.

C. G. Langton. Self-reproduction in cellular automata. Physica D, 10:135--144, 1984.

No context found.

C.G. Langton, Self-reproduction in cellular automata, Physica D, 10, 1984, 135144.

No context found.

Langton, C. G. (1984). Self-reproduction in cellular automata. Physica D, 10, 135--144.

No context found.

C. G. Langton. Self-reproduction in cellular automata. Physica D, 10:135--144, 1984.

No context found.

C. G. Langton, "Self-Reproduction in Cellular Automata," Physica D, vol. 10, pp. 135--144, 1984.

No context found.

C. G. Langton, "Self-Reproduction in Cellular Automata," Physica D, vol. 10, pp. 135--144, 1984.

No context found.

Langton, C.G., Self-reproduction in cellular automata, Physica, 10D, 135--144 (1984).

No context found.

Langton, C.G. (1984), "Self-Reproduction in Cellular Automata, " Physica D, vol. 10, pp. 135--144.

No context found.

Langton, C. G. "Self-reproduction in Cellular Automata ", Physica D, Vol. 10, pp. 135--144, 1984.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC