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 ....

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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 ....

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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 ....

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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 ....

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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.

....5(b) and 8(b) 4. 3 Relation to Previous Work Generally speaking, distributed agents as a model for computation is a newly explored area of research that studies the emergent behaviors in a lattice of finite automata in which autonomous agents react locally according to a set of behavioral rules [4, 10, 11, 12, 13, 14]. Shanahan [23] has investigated a class of evolutionary automata in which a population of agents evolves in a microworld of square grid locations. The characteristics of Shanahan s evolutionary automata consist in that a sequence of states in the microworld can be non deterministically generated ....

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

....machine using his 29 state two dimensional cellular automaton. Since then, various models of cellular automata that support self reproduction have been studied. For example, Codd [2] proposed an 8 state cellular model that has essentially the same ability as von Neumann s model. Langton [3] showed that, if universal computing and construction abilities are not required, a very simple self reproducing object can be designed in a modified 8 state model of Codd. We investigate here a problem whether self reproduction is possible in a two dimensional reversible cellular space. A ....

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

....of life. Its transition rules mean that reproduction and maintenance of life need proper population density of individuals. 3.3.2 Langton s self reproducing loop The most famous 2 dimensional CA which reproduces itself with simple transition function were reported by C.G. Langton in 1984. [7] Figure 3.3: Conway s game of LIFE (from [13] 2 2 2 2 2 2 2 2 2 1 7 0 1 4 0 1 4 2 2 0 2 2 2 2 2 2 0 2 2 7 2 2 1 2 2 1 2 2 1 2 2 0 2 2 1 2 2 7 2 2 1 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 0 7 1 0 7 1 0 7 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Figure 3.4: Langton s self reproducing loop (from [7] ....

....1984. 7] Figure 3.3: Conway s game of LIFE (from [13] 2 2 2 2 2 2 2 2 2 1 7 0 1 4 0 1 4 2 2 0 2 2 2 2 2 2 0 2 2 7 2 2 1 2 2 1 2 2 1 2 2 0 2 2 1 2 2 7 2 2 1 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 0 7 1 0 7 1 0 7 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Figure 3. 4: Langton s self reproducing loop (from [7]) The primitive life of this CA is shaped similar to a loop as figure 3.4. Each number is the state of the cell in the lattice and blank space means the state 0. Each cell can be 8 different states. The cells which have the state 2 are sheaths of the loop, and other cells surrounded by ....

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Langton, C.G. : Self-reproduction in cellular automata, Physica, D10, pp.135144 (1984).

....such complexity that, further simplifications notwithstanding, even today s state of the art computers lack the power to simulate it in its entirety. The next significant event in the history of self reproducing automata was the development of the automaton commonly referred to as Langton s loop [2]. By dropping the requirements of computational and constructional universality, Langton created an automaton capable of non trivial self replication, that is an automaton where the replication is actively directed by the automaton itself, rather than being a mere consequence of the transition ....

....machine, but the automaton retains a level of complexity too high for simulation. In fact, while parts of the machine have been successfully simulated, the task of simulating the whole automaton remains virtually impossible given current technology. 2. 2 Langton s loop Langton s automaton [2] is based on one of the components of Codd s universal constructor, namely the periodic emitter [3] The automaton (Fig. 2) is essentially a square loop, with internal and external sheaths, where the data necessary for the construction of a duplicate loop circulate counterclockwise. Duplication ....

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

.... for studying the behavior of complex, extended systems [von Neumann, 1966] It has been applied to the study of general phenomenological aspects of the world, including: communication, computation, construction, growth, reproduction, competition and evolution [Toffoli and Margolus, 1987, Langton, 1984, Burks, 1970, Smith, 1969] CAs also provide a means for modeling physical phenomena by reducing them to their basic, elemental laws (rules) Toffoli, 1980, Fredkin and Toffoli, 1982, Margolus, 1984, Vichniac, 1984, Bennett and Grinstein, 1985] CAs exhibit three notable features: massive ....

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

....machine, equivalent in power to a Turing machine. Later work by Codd [83] produced a self reproducing universal computing machine which required just 8 states per cell. Although simpler than von Neumann s, Codd s machine is still as complex as a modern digital computer. As noted by Langton [220], universality is a sufficient condition for self reproduction, however it is not a necessary condition. In his paper, Langton [220] describes a very simple self reproducing cellular automaton which is not based on the idea of a universal computing machine. Following the work of von Neumann, a ....

....which required just 8 states per cell. Although simpler than von Neumann s, Codd s machine is still as complex as a modern digital computer. As noted by Langton [220] universality is a sufficient condition for self reproduction, however it is not a necessary condition. In his paper, Langton [220] describes a very simple self reproducing cellular automaton which is not based on the idea of a universal computing machine. Following the work of von Neumann, a great deal of work was done in the 1960s on the theoretical aspects of various types of cellular automata, see [65, 402] In 1970, J H ....

C G Langton. Self-reproduction in cellular automata. In Farmer et al. [112], pages 135--144.

.... proof is quite elaborate and detailed in a book completed posthumously by von Neumann s colleague, Arthur Burks [ 8 ] A much simpler self replicating structure (though without universal constructing capabilities) was demonstrated by computer scientist Chris Langton, more than three decades later [ 4 ] . One of von Neumann s main conclusions was that the reproductive process uses the assembly instructions in two distinct manners: as interpreted code (during actual assembly) and as uninterpreted data (copying of assembly instructions to offspring) During the following decade, when the basic ....

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

....size, due mainly to their constructional universality, so it was impossible at that time to simulate them on computer 3 . They merely remained theoretical works. 3.4. 2 Searching for a minimal system capable of non trivial selfreplication The next epoch making work was done by Langton in 1984[27]. He thought of the constructional universality of automata as sufficient but not necessary condition for selfreproduction, and claimed that if the information structure explicitly directing selfreproduction existed in the structure of the organism, and if it was used in two different ....

....and instruction tapes like von Neumann s automaton, but their characteristic point is that the offspring automaton (middle) is constructed by the cooperation of two different kinds of the parent automata, i.e. F type (upper) and M type (lower) Figure 3. 4: Langton s self reproducing loop (from [27]) This model was implemented on 8 state CA with a von Neumann neighborhood. A signal sequence of 7 0 7 0 7 0 7 0 7 0 7 0 4 0 4 0 is set in a Q shaped tube structure enclosed by sheath state 2 s. Its details are introduced in section 4.4. Figure 3.5: Self reproductive process of Byl s small ....

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

....the computation and construction universality as the condition for a self reproducing machine to exclude passive or trivial replication of patterns in a cellular space. But, because of this condition, the early models [5, 22] needed huge configurations. Instead of the above condition, Langton [12] posed a new criterion only requiring that the construction of a daughter configuration should be actively directed by the parent configuration, and that information stored in the configuration must be treated in two different manners, i.e. interpreted and uninterpreted . Along this line, he ....

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

....this has prevented simulating them in their entirety. A different route was taken by Langton who observed that the above systems display sufficient capacity for self reproduction, and asked, conversely, what kind of logical organization is necessary for an automaton to be able to reproduce itself [Langton, 1984, Langton, 1986] He distinguished between trivial self reproduction, which is entirely coded 1 For those readers who are familiar with previous work on self reproduction in CAs we suggest a quick tour of the figures, by which a basic comprehension of our system may be gained. 2 The ....

....propagating down the arm, where it is translated as an instruction when it reaches the end of the arm. In executing the instructions the arm extends itself and folds, ultimately resulting in a daughter loop, also containing the genome needed to reproduce (Figure 2b. for a full description see [Langton, 1984]) A primary characteristic emphasized by Langton is the two different modes in which information is used, interpreted and uninterpreted, which also occur in natural self reproduction, the former being the process of translation, and the latter transcription. In Langton s loop, translation is ....

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

....directly in each cell (with a huge number of states) His 29 state construction was later further simplified by Codd (1968) to a CA with eight states per cell, and later by Banks (1971) to four states per cell. Von Neumann s design itself was implemented on a computer by Pesavento (1996) Langton (1984) studied very simple self reproducing structures in CAs in order to understand the minimal requirements for non trivial self reproduction. Other types of self reproducing automata (or computer programs) can be designed for example, see Hofstadter (1979) Chapter 16, for a discussion of ....

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

....by development from an egg , most models suffer from overcrowding such that an individual self reproducer can only reproduce once (or a small number of times) before it runs out of space in which to place its offspring, etc. Much of the recent work concerning self reproduction in CAs (e.g. [28, 24, 48, 36, 39]) also has this non biological character. In fact, as pointed out by Barry McMullin, much of the recent work in this area does not even seem to share von Neumann s concern with the evolution of increased complication, but addresses the problem of self reproduction in and of itself [32] On top ....

....(and therefore universal computation) and why it was designed in such a way that it could withstand some kinds of mutation so that it could evolve into a machine that performed other tasks as well as universal construction. Much of the recent work on self reproduction in CAs, starting with [28], has dropped this requirement for universal construction, but, as mentioned above, at the price of the reproducing machines being able to evolve by stepwise mutations into an unlimited variety of viable forms. Also, having dropped the requirement for universal construction, it is hard to offer a ....

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

....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 ....

....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 offspring, 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.

....general issue of multi cellular organisms versus uni cellular ones. The cellular space considered throughout this section is 3 state, 9 neighbor where states are denoted f0; 1; bg. 3. 1 A self reproducing loop Our first example involves a simple self reproducing loop motivated by Langton s work [Langton, 1984, Langton, 1986] who described such a structure in uniform cellular automata. His loop was later simplified by [Byl, 1989, Reggia et al. 1993] Langton s loop (motivated by [Codd, 1968] makes dual use of the information contained in a description to reproduce itself. The structure consists of a ....

....latter transcription. In Langton s loops translation is accomplished when the instruction signals are executed as they reach the end of the construction arms, and upon the collision of signals with other signals. Transcription is accomplished by the duplication of signals at the arm junctions [Langton, 1984]. 1 Throughout this paper we use the terms operational cell and operational rule interchangeably. The loop considered in this section consists of five cells and reproduces within six time steps . The initial configuration consists of a grid of vacant cells (i.e. with no rule) with a single ....

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

....it exists, but not shown. Thus, Langton began his quest to achieve this goal. Codd[16] proved that as few as 8 states could be used implement a self replicating CA. Langton was able to build a functional 8 state CA which could self reproduce. The details of this are presented in his 1983 paper[37]. Langton also explored the idea of a single parameter to describe the sweet spot where the Wolfram type IV CA lived[39] While it can be argued that a single parameter is too much of a reduction to use as a description[41] the idea of life as a dance on the shores of randomness had ....

C. G. Langton. Self reproduction in cellular automata. In F. D., T. T., and W. S., editors, Cellular Automata: Proceedings of an Interdiciplinary Workshop, pages 135--144. North Holland Physics Publishing, 1983.

....computation and construction universality to exclude passive or trivial replication of patterns in a cellular space. But, because of this constraint, the models mentioned above [9, 11, 45, 50] need huge number of cells to perform self reproduction. Instead of the von Neumann s condition, Langton [26] posed a new criterion only requiring that the construction of a daughter configuration should be actively directed by the mother, and that information stored in the configuration (i.e. genetic code ) must be treated in two different manners: interpreted and uninterpreted . Under this ....

....to exclude passive replication of patterns like a crystal growth. However, because of this condition, his self reproducing object in the 29 state cellular space was very huge in its configuration size [45] Later, Langton relaxed this condition, and proposed a very simple self reproducing CA model [26]. Namely, he removed the constraint that a self reproducing machine should have a computing ability, and posed a criterion only requiring that the self reproduction should be actively controlled by a mother machine by processing a genetic code of itself in two manners: i.e. decoding it to make a ....

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

....each cell can be in one of 29 states rather than just two. In 1984 Christopher Langton observed that although the capacity for universal construction is a sufficient condition for self replication, it is not a necessary one; furthermore, natural systems are not capable of universal construction. Langton (1984) and his successors Byl (1989) Reggia et al. 1993) and Morita and Imai (1997) developed self replicating automata which are much simpler than the universal constructor. These machines, however, lack any computing and constructing capabilities, their sole functionality being that of ....

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

....as applied to digital image processing is a newly explored area of research that studies the emergent behaviors in a lattice where agents react to the digital image environment according to a set of behavioral rules. It may be viewed as a further extension to the earlier work on cellular automata [8, 17, 18, 19, 22, 24]. Cellular automata, which drew upon Von Neumann s model [31] is concerned primarily with the fixed point properties in a lattice of finite automata in which cells act locally according to a set of cellular rules [22] Shanahan [33] investigated a class of cellular automata in which a population ....

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

....latter transcription. In Langton s loops translation is accomplished when the instruction signals are executed as they reach the end of the construction arms, and upon the collision of signals with other signals. Transcription is accomplished by the duplication of signals at the arm junctions (Langton 1984). The loop considered in this section consists of five cells and reproduces within six time steps . The initial configuration consists of a grid of vacant cells (i.e. with no rule) with a single loop composed of five cells in state 1, each containing the (same) loop rule (Figure 2a) The arm ....

....cell. The new configuration then acts as data to the arm, thereby providing the description by which the loop form is replicated. When a loop finds itself blocked by other loops it dies by retracting the construction arm. Figure 2b shows the configuration after several time steps. In his paper Langton (1984) compares the selfreproducing loop with the works of von Neumann (1966) 11 11 11 11 111 1110 11100 11101 1 time = 0 time = 1 time = 2 time = 3 1 11 11 11 11101 11011 11 11 11 11 11 1 1 0 time = 4 time = 5 time = 6 (a) time = 12 time = 66 A black square represents a cell in state 1, a non filled ....

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

....evolution process. Such experiments are needed to abstract the universal laws of evolution from the casual contingencies of the history of the earth. The first steps in this direction were the cellular automata (CA) of von Neumann [14] who only studied self replication. Among other, Langton [3] and Sipper [11] also addressed the question of evolution. Meanwhile Rasmussen et al. 7, 6] showed that a completely different model, inspired from computer architecture, could also be used in this domain. These ideas inspired T. Ray s Tierra simulator [8] providing the most spectacular ....

C.G. Langton. Self-reproduction in cellular automata. Physica D, 10(1-2):135--144, 1984.

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

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

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

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

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

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

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

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

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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.

No context found.

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

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