The techniques known as Cellular Automata (CA) can be used to create a variety of visual effects. As the state space for each cell, 24-bit photo realistic color was used. Several new state transition rules were created to produce unusual and beautiful results, which can be used in an interactive program or for special effects for images or videos. This chapter presents a technique for applying CA rules to an image at several different levels of resolution and recombining the results. A “soft” artistic look can result. The concept of “targeted” CAs is introduced. A targeted CA changes the value of a cell only if it approaches a desired value using some distance metric. This technique is used to transform one image into another, to transform an image to a distorted version of itself, and to generate fractals. The author believes that the techniques presented can form the basis for a new artistic medium that is partially directed by the artist and partially emergent. Images and animations from this work are posted on the World Wide Web at (http://www.scruznet.com/~hughes/CA.html). All cellular automata (CA) operate on a space of discrete states. The simplest CAs, such as the Game of Life, use a 1-bit state space. Most modern personal computers represent color as a 24-bit value, allowing for approximately 16 million possible colors. The work presented in this chapter uses a 24-bit color space that is represented in a 32-bit-long integer. This color space can be conceptualized as a three-dimensional bounded continuous vector space. Often, it is desirable to work with in the HSV (Hue, Saturation, Value) color space. Some of the rules encode the value (luminance) of a cell in the otherwise unused 8 high-order bits of a 32-bit word. The hue and saturation can be estimated “on the fly” with simple, fast algorithms. The hue is represented as an angle on the color wheel. For some rules, it is necessary to know the “distance” between two colors. Estimating the distance in perceptual space would be a difficult problem, as it would be dependent on the monitor used and the gamma exponent applied for a particular setup.
Chaos Control in Three Dimensional Cancer Model by State Space Exact Linearization Based on Lie Algebra
