scholarly journals Symmetry in Gardens of Eden

10.37236/2611 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Christiaan Hartman ◽  
Marijn J. H. Heule ◽  
Kees Kwekkeboom ◽  
Alain Noels

Conway's Game of Life has inspired enthusiasts to search for a wide range of patterns for this classic cellular automaton. One important challenge in this context is finding the smallest Garden of Eden (GoE), a state without a predecessor. We take up this challenge by applying two techniques. First, we focus on GoEs that contain a symmetry. This significantly reduces the size of the search space for interesting sizes of the grid. Second, we implement the search using incremental satisfiability solving to check thousands of states per second. By combining these techniques, we broke several records regarding GoEs: the fewest defined cells, the smallest bounding box, and the lowest living density. Furthermore, we established a new lower bound for the smallest GoE.

2015 ◽  
Vol 21 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Randall D. Beer

Maturana and Varela's concept of autopoiesis defines the essential organization of living systems and serves as a foundation for their biology of cognition and the enactive approach to cognitive science. As an initial step toward a more formal analysis of autopoiesis, this article investigates its application to the compact, recurrent spatiotemporal patterns that arise in Conway's Game-of-Life cellular automaton. In particular, we demonstrate how such entities can be formulated as self-constructing networks of interdependent processes that maintain their own boundaries. We then characterize the specific organizations of several such entities, suggest a way to simplify the descriptions of these organizations, and briefly consider the transformation of such organizations over time.


Author(s):  
Kent Fenwick

John Conway’s Game of Life, published in Scientific American in 1970 is an attempt to model the behavior  of life using a 2D cellular automaton. Although a breakthrough discovery for cellular automata and  emergence theory, the game is restricted and incomplete due to its static, simplified rules. We will show that the game does not model life accurately and propose an alternative: TrueLife. TrueLife is a non­  deterministic, non­local, evolving Game of Life variant that we believe is more complete than Life for  several key reasons. TrueLife is unique since at each generation a rule is chosen randomly from a list and  applied to the current state. This allows the game to be inherently non­deterministic since it is impossible to know which rule is being applied at a given iteration. TrueLife will also be a learning simulation where rules that produce better results will be applied more frequently. Another unique aspect of TrueLife is the motivation behind the rules. The original Life rules are Darwinian and selfish acting only on local inputs that lead to local outputs. TrueLife’s rules will be non­local and act globally across the entire grid. TrueLife’s rules were formalized by drawing on much broader areas of science such as ecology, psychology and quantum theory. We are currently in the process of finding a model system to which  TrueLife would be best suited.


2021 ◽  
Vol 15 (5) ◽  
pp. 1-32
Author(s):  
Quang-huy Duong ◽  
Heri Ramampiaro ◽  
Kjetil Nørvåg ◽  
Thu-lan Dam

Dense subregion (subgraph & subtensor) detection is a well-studied area, with a wide range of applications, and numerous efficient approaches and algorithms have been proposed. Approximation approaches are commonly used for detecting dense subregions due to the complexity of the exact methods. Existing algorithms are generally efficient for dense subtensor and subgraph detection, and can perform well in many applications. However, most of the existing works utilize the state-or-the-art greedy 2-approximation algorithm to capably provide solutions with a loose theoretical density guarantee. The main drawback of most of these algorithms is that they can estimate only one subtensor, or subgraph, at a time, with a low guarantee on its density. While some methods can, on the other hand, estimate multiple subtensors, they can give a guarantee on the density with respect to the input tensor for the first estimated subsensor only. We address these drawbacks by providing both theoretical and practical solution for estimating multiple dense subtensors in tensor data and giving a higher lower bound of the density. In particular, we guarantee and prove a higher bound of the lower-bound density of the estimated subgraph and subtensors. We also propose a novel approach to show that there are multiple dense subtensors with a guarantee on its density that is greater than the lower bound used in the state-of-the-art algorithms. We evaluate our approach with extensive experiments on several real-world datasets, which demonstrates its efficiency and feasibility.


2018 ◽  
Vol 8 (8) ◽  
pp. 1239 ◽  
Author(s):  
Carlos Villaseñor ◽  
Nancy Arana-Daniel ◽  
Alma Alanis ◽  
Carlos Lopez-Franco ◽  
Javier Gomez-Avila

The robotic mapping problem, which consists in providing a spatial model of the environment to a robot, is a research topic with a wide range of applications. One important challenge of this problem is to obtain a map that is information-rich (i.e., a map that preserves main structures of the environment and object shapes) yet still has a low memory cost. Point clouds offer a highly descriptive and information-rich environmental representation; accordingly, many algorithms have been developed to approximate point clouds and lower the memory cost. In recent years, approaches using basic and “simple” (i.e., using only planes or spheres) geometric entities for approximating point clouds have been shown to provide accurate representations at low memory cost. However, a better approximation can be implemented if more complex geometric entities are used. In the present paper, a new object-mapping algorithm is introduced for approximating point clouds with multiple ellipsoids and other quadratic surfaces. We show that this algorithm creates maps that are rich in information yet low in memory cost and have features suitable for other robotics problems such as navigation and pose estimation.


2012 ◽  
Vol 8 (S291) ◽  
pp. 233-233
Author(s):  
Heino Falcke ◽  

AbstractLOFAR is an innovative new radio interferometer operating at low radio frequencies from 10 to 270 MHz. It combines a large field-of-view, high fractional bandwidth, rapid response, and a wide range of baselines from tens of meters to thousand kilometers. Its use of phased-array technology and its digital nature make LOFAR an extremely versatile instrument to search for transient radio phenomena on all time scales. Here we discuss in particular the search for fast radio transients (FRATs) at sub-second time scales. In fact, at these time scales the radio sky is rather dynamic due to coherent emission processes. Objects like pulsars, flaring stars, or planets like Jupiter are able to produce bright short flares. For pulsars, most previous detection strategies made use of the rotation of pulsars to detect them, using Fourier techniques, but it is also possible to detect pulsars and other objects through their single pulses. Such surveys have, e.g., led in the previous decade to the detection of Rapid Radio Transients (RRATS), but the unprobed search space is still rather large. LOFAR is now conducting a rather unique survey over the entire northern sky, searching for bright dispersed single radio pulses. This FRATs survey makes use of the LOFAR transient buffer boards (TBBs), which had initially been used to detect nanosecond radio pulses from cosmic rays. The TBBs store the radio data from each single receiver element of LOFAR and allow one to look back in time. A trigger system that runs parallel to normal imaging observation allows one to detect single pulses in an incoherent beam of all LOFAR stations, covering several tens to hundred square degrees at once. Once triggered, the data can be used to localize the pulse and to discriminate cosmic sources from terrestrial interference through 3D localization. The system has been successfully tested with known pulsars and first results of the ongoing survey will be presented.


2021 ◽  
pp. 174702182110503
Author(s):  
Alastair David Smith ◽  
Carlo De Lillo

Search – the problem of exploring a space of alternatives in order to identify target goals – is a fundamental behaviour for many species. Although its foundation lies in foraging, most studies of human search behaviour have been directed towards understanding the attentional mechanisms that underlie the efficient visual exploration of two-dimensional scenes. With this review, we aim to characterise how search behaviour can be explained across a wide range of contexts, environments, spatial scales, and populations, both typical and atypical. We first consider the generality of search processes across psychological domains. We then review studies of interspecies differences in search. Finally, we explore in detail the individual and contextual variables that affect visual search and related behaviours in established experimental psychology paradigms. Despite the heterogeneity of the findings discussed, we identify that variations in control processes, along with the ability to regulate behaviour as a function of the structure of search space and the sampling processes adopted, to be central to explanations of variations in search behaviour. We propose a tentative theoretical model aimed at integrating these notions and close by exploring questions that remain unaddressed.


2021 ◽  
Vol 13 (19) ◽  
pp. 3865
Author(s):  
Yongqiang Zhang ◽  
Dongryeol Ryu ◽  
Donghai Zheng

Remotely sensed geophysical datasets are being produced at increasingly fast rates to monitor various aspects of the Earth system in a rapidly changing world. The efficient and innovative use of these datasets to understand hydrological processes in various climatic and vegetation regimes under anthropogenic impacts has become an important challenge, but with a wide range of research opportunities. The ten contributions in this Special Issue have addressed the following four research topics: (1) Evapotranspiration estimation; (2) rainfall monitoring and prediction; (3) flood simulations and predictions; and (4) monitoring of ecohydrological processes using remote sensing techniques. Moreover, the authors have provided broader discussions, on how to make the most out of the state-of-the-art remote sensing techniques to improve hydrological model simulations and predictions, to enhance their skills in reproducing processes for the fast-changing world.


1993 ◽  
Vol 48 (5) ◽  
pp. 3345-3351 ◽  
Author(s):  
J. B. C. Garcia ◽  
M. A. F. Gomes ◽  
T. I. Jyh ◽  
T. I. Ren ◽  
T. R. M. Sales

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