Application of Cellular Automata for a Generative Art System

In this article, the author describes a study that proposes the use of cellular automata (CA) as a useful tool for a creative pattern-generating art system. A one-rule firing CA is used to efficiently represent basic CA patterns. The key idea in this method is to mix basic patterns in order to design complex patterns. Two types of mixing—iterative and hierarchical—are introduced. The results are demonstrated through example patterns, including ornamental and tiling patterns. The concept of an expanded neighborhood is introduced and applied to the generation of flower-like images. The author concludes with several suggestions for future research topics in relation to the proposed method.

A computerized system used to generate artistic patterns is called a generative art (GA) system [1,2] or a computational aesthetics system [3]. Recent GA systems frequently employ evolutionary algorithms to grow complex patterns from initial random seeds [4]. Embryogeny can be classified into three types: external, explicit and implicit [5]. Among these three types, implicit embryogeny is closest to a biological system, wherein the patterns are not predetermined. This approach uses highly indirect chains of interacting rules to generate complex patterns.

Cellular automata (CA)–based systems can be faithful to the definition of implicit embryogeny because the rules of CA do not directly define the patterns. A CA system is commonly used to generate interesting patterns using computers. Rule-based CA systems have been used to generate patterns such as snow crystals [6,7] and color patterns of mollusks [8]. In addition to the traditional types of CA, variants of CA have been applied in aesthetic pattern design systems including ant-type systems [9], reaction-diffusion systems [10,11] and recursive CA systems [12]. Because a CA-like system can be easily interpreted as directly operating on the minimum unit of the computer screen (i.e. the pixels), it is expected that the system can generate patterns free from model biases. Hence, the system is made to be autonomous and independent, which are required characteristics of a GA system [3]. However, despite such advantages, the full potential of CA systems remains to be investigated. I suggest a new method for applying CA to the design of aesthetically interesting patterns. The proposed method is based on a new kind of CA system called one-rule firing [13,14].