Abstract
The aim of this chapter is to explore a classic stochastic problem using the tools of the graphics environment. Stochastic processes are associated with the concepts of uncertainty or chance. Major areas of research in mathematical and applied sciences, statistics, finance, and artificial intelligence/machine learning benefit from the knowledge gained studying this process. Visual Art also depends on elements of uncertainty and chance. To explore the commonality of concern between Science and Art and better understand stochastic processes, the author organizes his research according to the Knowledge Visualization framework, examines a graph theory reference model called the “shortest route problem,” and, adding additional elements specific to the art-making process, shares his results to highlight the relevance of interdisciplinary studies in the fields of randomness and visual perception.
TopIntroduction
Randomness by nature is challenging to define.
Many people associate randomness with unpredictability: the randomness of the shuffling of a deck of cards or the randomness of the playing of a musical instrument. However, they are not both equally random. We can use randomness to make choices less predictable. Yet, unpredictability is more than mere randomness; it is an opportunity to select or create a pattern more or less predictable: something that can be easily detected.
According to the Wolfram definition, the word random is synonymous with the term stochastic. It is of Greek origin and means “pertaining to chance”. The term stochastic has been used in the past to differentiate art practices such as medicine or rhetoric in which the knowledge and skill of the practitioner cannot be measured by the direct result of their work as in most other applied sciences. Today, both terms designate events that are variable or carry unforeseeable outcome.
Science, specifically mathematics, is based on objectivity and hard facts. Its relationship to randomness has always been challenging because of the underlying difference between randomness and uncertainty. For example, randomness can be used to get a very accurate forecast, and uncertainty can be used to get a very reliable forecast, though this is harder and takes longer.
In mathematics, Snell (1997) in a conversation with Joe Doob points out that every non-mathematical probabilistic assertion suggests a mathematical counterpart that sharpens the formulation of the non-mathematical assertion.
The theory of probability, to which the concept of random processes is attached, was introduced by David Lewis in 1884, and later adopted by Charles Darwin, Alfred Wegener, Werner Heisenberg, and many others. Today this field of research has opened to broader and more complex investigation in the area of applied mathematics, mathematical physics, mathematical biology, control theory, and engineering.
Mathematicians Richard Courant and Herbert Robbins (1996) state that Mathematics offers science both a foundation of truth and a standard of certainty based on precision and rigorous proof. Mathematics exacting standards helped pave the way to explore stochastic processes in an objective factual and repeatable manner. Russian mathematician Kolmogorov initiated its study some 70 years ago. Based on Greek axiomatic geometry, it explores the logic of shape, quantity and arrangement.
Shape, quantity, and arrangement are part of the visual artist vocabulary. To a certain extent, the art-making process, its perception, and appreciation depend on a set of random elements, in this case pertaining to light, optical alertness, and various additional physical and cultural parameters. As the world is seeing more research on visualization, we’re starting to recognize that learning to understand, read, and interpret an image is a good way to get a deep insight in the subject being studied.
Using a scientific approach to study randomness in art seems like a promising way to understand the medium better: good visualizations are the ones that can be composed and read only if the creator has the knowledge and experience to know what they are. Knowledge visualization is one tool helping achieve this goal.
Knowledge Visualization is a framework that examines the use of visual representations to improve the creation and transfer of knowledge, stated Meyer (2009). Burkhard (2013) in a seminal paper on the structure of the framework describes it as a tool to investigate the power of visual formats to represent knowledge, whose aim is to support cognitive processes in generating, structuring, using, and sharing knowledge. Knowledge visualization facilitates the creation and transfer of knowledge between individuals and groups by giving the originators richer means of expressing what they know.
Following the framework guidelines, I collected information from various scientific sources to understand, interpret, create, and share new information on the study of stochastic processes from the perspective of a graphics and visual communication designer.
To illustrate my point, I selected a model used by Professor of Management Science Evan L. Porteus (2002) to demonstrate the calculation involved in solving a stochastic random process. I broke down each element of the statistical model into separate objects, recombined them according to the scientific narrative, and added distinct components pertaining specifically to a visual communication methodology.
Key Terms in this Chapter
After-Effect: The motion aftereffect illusion has been known since ancient Greek times. It has been studied extensively by psychologists however the cause is still not fully understood. Some researchers attribute the effect to the adaptation by specific neurons in the visual cortex responsible for the perception of motion. As long as the neural net is active, the brain will automatically make the neural networks, networks that have already learned, more similar to what the original scene was, by means of comparison.
Information: It is a form of data that is accurate and timely, specific and organized for a purpose, presented within a context that gives it meaning and relevance, and can lead to an increase in understanding and decrease in uncertainty.
GPT-2: Modern neural network and a language model that generates coherent paragraphs of text one word at a time. The objective of the model is to create a list of strings where the strings are each sorted by ascending priority. The function then selects a random string from this list and updates the priority of each element. Once the strings are sorted, the function can then return a string with a new priority value. And so on.
Hue: Hue refers to the pure spectrum of color: red, orange, yellow, blue, green violet. In visual art, all hues can be mixed from three basic hues: red, blue, yellow, known as primaries. When pigment primaries are all mixed together, the result is black.
Voronoi: A Voronoi diagram, named after Russian mathematician Georgy Voronoi, partitions the space based on the minimal distance to each site. Voronoi diagrams can be used for discretization of the surface as well as space. Inspiration with these structures results in development of two- and three-dimensional structural elements that can be used in computer graphics, architectural design and urban planning.
Recursive Thinking: The process of solving large problems by breaking them down into smaller, simpler problems that have identical forms.
Algorithm: An algorithm is a sequence of steps that describe how a problem can be solved. It is a set of self-contained sequence of instructions or actions that contains finite space or sequence and that will give us a result to a specific problem in a finite amount of time. If X0 has been identified, then a program which uses a program (X0) to generate an output, i.e., X1, is said to be implemented using an Algorithm.
Stochastic Problem: Stochastic problems are mathematical problems where some of the data incorporated into the objective is uncertain. Un- certainty is usually characterized by a probability distribution on the parameters.
Visual Communication: Visual Communication is a multidisciplinary field encompassing graphic design, illustration, fine arts (like drawing and painting), multimedia, and photography. Visual communication applies the fundamentals of major art forms and art techniques to solve communication problems.
Information Visualization: Aims to explore large amounts of abstract data to get new insights or make the stored data more readily accessible.
Volume: In the context of this paper, volume references scientific visualization, computer graphics rendering, and various set of techniques used to display a 2D projection of a 3D object.
Random Processes: A random process models the progression of a system over time, where the evolution is random rather than deterministic. Random processes are used in a variety of fields including economics, finance, engineering, physics, and biology.
Value: Value defines the intensity of a color in terms of lightness or darkness. It helps artists and designers to define form and creates spatial illusions on a two-dimensional surface. Contrast of value separates objects in space; gradation of value suggests mass and contour of a contiguous surface.
Chance: Chance and probability have a similar meaning. Generally, “ chance ” refers to a random event, And probability usually refers to the likelihood that some random event will occur before the actual event occurs. The likelihood is that, when looking at the distribution of a certain event, the chances of it happening is higher or lower than the probability of it happening. Probability is expressed in numbers or percentages, chance is more likely to be used in common day language.
Knowledge Visualization: Knowledge visualization facilitates the creation and transfer of knowledge by giving users an extended palette of tools to express and share what they know. This framework aims at supporting cognitive processes in creating and sharing knowledge. It uses visual analysis based on the study of perception and incorporates Information Visualization. It is a compelling way to both understand what is seen and explained what has been witnessed.
Graph Theory: Graph theory is about the relationship between lines and points. A graph consists of some points and some lines between them. No attention is paid to the position of points and the length of the lines.
Neuroscience: Scientific study of the nervous system. In the context of this paper, Neuroscience findings in the study of brain mechanisms and neural representations in the human visual cortex helped define the parameter by which this work was completed.
Chroma: Defines the strength or dominance of a hue and its saturation. Variations in Chroma can be achieved by adding different amounts of a neutral gray of the same value to alter a color. CIELAB: CIELAB is the second of two systems adopted by the CIE. CIE 1931 RGB and CIE 1931 XYZ color spaces are the first mathematically defined color spaces. The International Commission on Illumination(CIE) created them in 1931. CIELAB is an opponent color system based on the earlier system of Richard Hunter. Like all CIE models, it is device independent and is used for color management as the device independent model of the ICC (International Color Consortium) device profiles.
Perception: Perception is the ability to understand external stimuli. Visual perception is the ability to detect light and interpret it as the perception known as sight or vision. Vision has a specific sensory system, the visual system. Because what people see is not simply a translation of retinal stimuli, it is the object of constantly evolving studies in the field of neuroscience.