Binary Pattern
Binary patterns refer to images created using the binary number system, which operates on a base-2 numeral system utilizing only two symbols: 0 and 1. Unlike the decimal system, which is based on ten digits, binary patterns leverage the simplicity and efficiency of this two-symbol system, particularly in computing and digital media. In a standard 32-bit representation, images are composed of pixels, each containing 32 bits of information that dictate color and transparency in the RGBA (Red Green Blue Alpha) color space. This allows for complex images to be represented while saving memory by storing the process or formulas used to create them, rather than encoding each pixel individually.
The binary system has a rich historical context, with applications ranging from decision-making to encryption, and it plays a crucial role in the functioning of modern electronic devices. By employing Boolean algebra, which uses true or false variables, computers can perform bitwise operations on binary numbers quickly and efficiently. The resulting binary patterns can range from simple shapes to intricate designs, making them versatile for various visual applications, including computer operating systems that use these patterns for tiles and backgrounds. Overall, binary patterns exemplify the intersection of mathematics, computer science, and visual art, showcasing the potential of binary systems in digital representation.
On this Page
Subject Terms
Binary Pattern
The binary number system is the more common name for the base-2 numeral system. Unlike the base-10, or decimal system, which uses digits 0-9 to represent numeric values, the binary number system uses only two symbols, traditionally 0 and 1. Thus the binary representations of base-10 "1, 2, 3" are "1, 10, 11." The binary system is used in computers and other electronics because of its ease of representation with two-state devices such as electrical switches. Throughout history, binary systems have had many uses, including decision making (coin-flipping returns one of two values), divination (the I Ching uses yin/yang system), and encryption (Morse code uses short and long tones), in addition to mathematical applications. Boolean algebra, which became integral to the design of circuitry and computers, was developed by George Boole in 1854 and performs operations with variables assigned the values true or false.
Binary numbers may be manipulated either by conventional arithmetic methods or by using Boolean logical operators in what is usually called a bitwise operation. Bitwise operations are performed by the processor on the individual binary numerals, or bits, of a computer system and are faster and more efficient than arithmetic methods. When computers perform binary operations that result in a 32-bit integer, these operations can be used to form images called binary patterns.
Overview
Despite their underlying simplicity, images formed by binary patterns may appear quite complex. The 32-bit value is key because 32 bits are used in RGBA (Red Green Blue Alpha) color space, in which 8 bits are devoted to the amount of red, green, and blue in an image, with a further 8 bits in the alpha channel reserved for the image's degree of transparency. Images displayed on computers, television screens, and other LCD screens are made up of pixels, each of which is the smallest physical point on the screen. Pixels are not a standard size, however—in comparing two different same-size screens, the one with the highest resolution has the smallest pixels, and thus a greater number of adjustable points.) These pixels are like incredibly tiny dabs of paint adding up to make a coherent image. In a 32-bit RGBA color space, each pixel is associated with 32 bits of information determining its color and transparency.
Binary patterns can form images that take up much less space in memory than if each pixel were encoded individually, by instead storing the formula or series of binary operations used to form the image. Many computer operating systems include basic patterns and tiles that take up a fraction of the space of an image like a photograph, which can't be reconstructed by binary operations. They may be simple repeated shapes, or intricate patterns reminiscent of murals and mandalas.
Bibliography
Kolo, Brian. Binary and Multiclass Classification. New York: Weatherford, 2010.
Kjaerulff, Uffe, and Anders Madsen. Bayesian Networks and Influence Diagrams. New York: Springer, 2014.
Larcher, Gerhard, and Friedrich Pilichshammer, eds. Applied Algebra and Number Theory. New York: Cambridge UP, 2015.
Marchand-Maillet, S. Binary Digital Image Processing. Waltham, MA: Academic P, 1999.
Nicholas, Patrick. Scala for Machine Learning. New York: Packt, 2014.
Reba, Marilyn, and Douglas R. Shier. Puzzles, Paradoxes, and Problem Solving. New York: Chapman, 2014.
Stakhov, Alexey, and Scott Anthony Olsen. The Mathematics of Harmony. Hackensack: World Scientific, 2009.
Yager, Ronald, and Ali Abbasov, eds. Soft Computing. New York: Springer, 2014.