Mohammad Ali Javaheri Javid

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.

Detecting Symmetry in Cellular Automata Generated Patterns Using Swarm Intelligence

Since the introduction of cellular automata in the late 1940’s 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 patterns 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 axes of symmetry in the cellular automata generated patterns.

On Symmetry, Aesthetics and Quantifying Symmetrical Complexity

The concepts of order and complexity and their quantitative evaluation have been at the core of computational notion of aesthetics. One of the major challenges is conforming human intuitive perception and what we perceive as aesthetically pleasing with the output of a computational model. Informational theories of aesthetics have taken advantage of entropy in measuring order and complexity of stimuli in relation to their aesthetic value. However entropy fails to discriminate structurally different patterns in a 2D plane. In this work, following an overview on symmetry and its significance in the domain of aesthetics, a nature-inspired, swarm intelligence technique (Dispersive Flies Optimisation or DFO) is introduced and then adapted to detect symmetries and quantify symmetrical complexities in images. The 252 Jacobsen & Hofel’s images used in this paper are created by researchers in the psychology and visual domain as part of an experimental study on human aesthetic perception. Some of the images are symmetrical and some are asymmetrical, all varying in terms of their aesthetics, which are ranked by humans. The results of the presented nature-inspired algorithm is then compared to what humans in the study aesthetically appreciated and ranked. Whilst the authors believe there is still a long way to have a strong correlation between a computational model of complexity and human appreciation, the results of the comparison are promising.

Analysis of information gain and Kolmogorov complexity for structural evaluation of cellular automata configurations

ABSTRACT Shannon entropy fails to discriminate structurally different patterns in two-dimensional images. We have adapted information gain measure and Kolmogorov complexity to overcome the shortcomings of entropy as a measure of image structure. The measures are customised to robustly quantify the complexity of images resulting from multi-state cellular automata (CA). Experiments with a two-dimensional multi-state cellular automaton demonstrate that these measures are able to predict some of the structural characteristics, symmetry and orientation of CA generated patterns.

Information gain measure for structural discrimination of cellular automata configurations

Cellular automata (CA) are known for their capability in exhibiting interesting emergent behaviour and capacity to generate complex and often aesthetically appealing patterns through the local interaction of rules. Mean information gain has been suggested as a measure of discriminating structurally different two-dimensional (2D) patterns. This paper addresses quantitative evaluation of the complexity of CA generated configurations. In particular, we examine information gain as a spatial complexity measure for discriminating multi-state 2D CA generated configurations. 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 symmetries and randomness of 2D CA patterns.

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.

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.