A Comparative Analysis of Detecting Symmetries in Toroidal Topology

In late 1940s and with the introduction of cellular automata, various types of problems in computer science and other multidisciplinary fields have started utilising this new technique. The generative capabilities of cellular automata have been used for simulating various natural, physical and chemical phenomena. Aside from these applications, the lattice grid of cellular automata has been providing a by-product interface to generate graphical patterns for digital art creation. One notable aspect of cellular automata is symmetry, detecting of which is often a difficult task and computationally expensive. This paper uses a swarm intelligence algorithm—Stochastic Diffusion Search—to extend and generalise previous works and detect partial symmetries in cellular automata generated patterns. The newly proposed technique tailored to address the spatially-independent symmetry problem is also capable of identifying the absolute point of symmetry (where symmetry holds from all perspectives) in a given pattern. Therefore, along with partially symmetric areas, the centre of symmetry is highlighted through the convergence of the agents of the swarm intelligence algorithm. Additionally this paper proposes the use of entropy and information gain measure as a complementary tool in order to offer insight into the structure of the input cellular automata generated images. It is shown that using these technique provides a comprehensive picture about both the structure of the images as well as the presence of any complete or spatially-independent symmetries. These technique are potentially applicable in the domain of aesthetic evaluation where symmetry is one of the measures

Swarm intelligence approach in detecting spatially-independent symmetries in cellular automata

In late 1940's and with the introduction of cellular automata, various types of problems in computer science and other multidisciplinary fields have started utilising this new technique. The generative capabilities of cellular automata have been used for simulating various natural, physical and chemical phenomena. Aside from these applications, the lattice grid of cellular automata has been providing a by-product interface to generate graphical patterns for digital art creation. One notable aspect of cellular automata is symmetry, detecting of which is often a difficult task and computationally expensive. This paper uses a swarm intelligence algorithm - Stochastic Diffusion Search - to extend and generalise previous works and detect partial symmetries in cellular automata generated patterns. The newly proposed technique tailored to address the spatially-independent symmetry problem is also capable of identifying the absolute point of symmetry (where symmetry holds from all perspectives) in a given pattern. Therefore, along with partially symmetric areas, the centre of symmetry is highlighted through the convergence of the agents of the swarm intelligence algorithm. This technique is potentially applicable in the domain of aesthetic evaluation where symmetry is one of the measures

Swarmic approach for symmetry detection of cellular automata behaviour

Since the introduction of cellular automata in the late 1940s they have been used to address various types of problems in computer science and other multidisciplinary fields. Their generative capabilities have been used for simulating and modelling various natural, physical and chemical phenomena. Besides these applications, the lattice grid of cellular automata has been providing a by-product interface to generate graphical contents for digital art creation. One important aspect of cellular automata is symmetry, detecting of which is often a difficult task and computationally expensive. In this paper a swarm intelligence algorithm—Stochastic Diffusion Search—is proposed as a tool to identify points of symmetry in the cellular automata-generated patterns

The discrete dynamics of small-scale spatial events: agent-based models of mobility in carnivals and street parades

Small-scale spatial events are situations in which elements or objects vary in such away that temporal dynamics is intrinsic to their representation and explanation. Someof the clearest examples involve local movement from conventional traffic modelingto disaster evacuation where congestion, crowding, panic, and related safety issue arekey features of such events. We propose that such events can be simulated using newvariants of pedestrian model, which embody ideas about how behavior emerges fromthe accumulated interactions between small-scale objects. We present a model inwhich the event space is first explored by agents using ?swarm intelligence?. Armedwith information about the space, agents then move in an unobstructed fashion to theevent. Congestion and problems over safety are then resolved through introducingcontrols in an iterative fashion and rerunning the model until a ?safe solution? isreached. The model has been developed to simulate the effect of changing the route ofthe Notting Hill Carnival, an annual event held in west central London over 2 days inAugust each year. One of the key issues in using such simulation is how the processof modeling interacts with those who manage and control the event. As such, thischanges the nature of the modeling problem from one where control and optimizationis external to the model to one where this is intrinsic to the simulation

A quantitative approach for detecting symmetries and complexity in 2D plane

Aesthetic evaluation of computer generated patterns is a growing filed with several challenges. This paper focuses on the quantitative evaluation of order and complexity in multi-state two-dimensional (2D) cellular automata (CA). CA are known for their ability to generate highly complex patterns through simple and well defined local interaction of rules. It is suggested that the order and complexity of 2D patterns can be quantified by using mean information gain. This measure, also known as conditional entropy, takes into account conditional and joint probabilities of the elements of a configuration in a 2D plane. A series of experiments is designed to demonstrate the effectiveness of the mean information gain in quantifying the structural order and complexity, including the orientation of symmetries of multi-state 2D CA configurations

Bits from Biology for Computational Intelligence

Computational intelligence is broadly defined as biologically-inspired computing. Usually, inspiration is drawn from neural systems. This article shows how to analyze neural systems using information theory to obtain constraints that help identify the algorithms run by such systems and the information they represent. Algorithms and representations identified information-theoretically may then guide the design of biologically inspired computing systems (BICS). The material covered includes the necessary introduction to information theory and the estimation of information theoretic quantities from neural data. We then show how to analyze the information encoded in a system about its environment, and also discuss recent methodological developments on the question of how much information each agent carries about the environment either uniquely, or redundantly or synergistically together with others. Last, we introduce the framework of local information dynamics, where information processing is decomposed into component processes of information storage, transfer, and modification -- locally in space and time. We close by discussing example applications of these measures to neural data and other complex systems

Spatial complexity measure for characterising cellular automata generated 2D patterns

Cellular automata (CA) are known for their capacity to generate complex patterns through the local interaction of rules. Often the generated patterns, especially with multi-state two-dimensional CA, can exhibit interesting emergent behaviour. This paper addresses quantitative evaluation of spatial characteristics of CA generated patterns. It is suggested that the structural characteristics of two-dimensional (2D) CA patterns can be measured using mean information gain. This information-theoretic quantity, also known as conditional entropy, takes into account conditional and joint probabilities of cell states in a 2D plane. The effectiveness of the measure is shown in a series of experiments for multi-state 2D patterns generated by CA. The results of the experiments show that the measure is capable of distinguishing the structural characteristics including symmetry and randomness of 2D CA patterns