Krome Barratt, Logic & design in art, science & mathematics, New York: Design Books, 1980. A listing of some of the chapter titles will give a sense of the interest this work will have for imagists: same and similar, rhythm, progressions and growth, dynamic and harmonic series, ratio, proportion, scale, simple oscillatory structures, the moving point, lines and edges, a geometry of curves, dramatization. The chapters propose principles related to the concepts organized around the themes. Though the principles are not always obvious or convincingly established, the work is full of stimulating ideas, many of them useful in creating interesting visual images.

John Bowers, Introduction to two-dimensional design: Understanding form and function, New York: John Wiley & Sons, 1999. This is a quick read for a reader who wants a general introduction to some basic issues in color, form and meaning in two-dimensional design. With only 123 heavily illustrated pages, it cannot go into depth on any of its many topics, but it does provide references to some very good works. The reader is exposed to Gestalt theory (closure, continuance, proximity, and similarity), problem solving (learn conditions, identify and define the problem, generate ideas and select solutions, implement solution and evaluate result), ways of defining visual elements (dot, line, plane, voume), visual characteristics (size, shape, texture, color), and visual interactions (position, direction, space), color, composition and more. It’s price is a bit steep, but you should be able to find it in a good library.

Robert Dixon, Mathographics, New York: Dover Publications, 1991 (originally published by Oxford: Basil Blackwell 1987). This book presents the math and related details for drawing polygons, curves, spirals, daisies, waves, and other basic items. It illustrates with lots of drawings that can be easily implemented with simple computer programs. At times, it is frustrating that the techniques used to produce a particular drawing are not more specifically revealed. You get the feeling that you are using one of those high school texts that insist on giving answers only to the odd-numbered problems or that announces that a particularly interesting derivation is “left as an exercise to the reader.” Still, it is a very good starting point for someone who wants a quick, practical introduction to mathematically-based construction of simple objects.

Maitland Graves, The art of color and design, New York: McGraw-Hill Book Company, 1951. In part one of this work, Graves defines seven elements of design (line, direction, shape, size, texture, value, and color). In part two, he introduces eight principles (repetition, alternation, harmony, gradation, contrast, dominance, unity, and balance) and shows how the elements are related according to these principles. Finally, in part three, he analyzes the elements of design. What makes this work of particular interest to us is its vision. The book ends with discussions of the psychology of color, color hearing, color music, and abstract films. The latter section includes brief reference to the work or Leopold Survage, Viking Egling, Len Lye, and Oscar Fischinger, among others.

Scott McCloud, Understanding comics: The invisible art, New York: Harper Perennial, 1994. My first encounter with this book was when an Apple software engineer told me that it was the best book he had read on user-interface design. Cartooning is, of course, a sequential graphic art. Consequently, many of the author’s observations are applicable to lumia. Of particular interest are the chapters “Living in Line,” which explores the relationship between expressive style and emotion, and “A Word About Color.”

Clifford A. Pickover [Ed.], The pattern book: Fractals, art, and nature, Singapore: World Scientific, 1995. Pickover ‘s many books are filled with techniques, ideas, algorithms, and code that will fuel the imaginations and toolkits of imagists for a very long time. This book is a particularly dense collection of patterns, most of them mathematical and easily computed, that were submitted from people working in a broad variety of disciplines. It is a wonderful source book to which I return again and again.

Peter S. Stevens, Handbook of regular patterns: An introduction to symmetry in two dimensions, Cambridge: MIT Press, 1984. The basic operations of symmetry are introduced and then used to create point groups, the seven line groups, and the seventeen plane groups. Illustrations come from textiles, mosaics, building plans, nature, and M. C. Escher’s prints and drawings.

Wucius Wong, Principles of two-dimensional design, New York: John Wiley & Sons, 1972. This book deals with two-dimensional design at an abstract level. It’s chapters on form, repetition, structure, similarity, gradtion, radiation, anomaly, contrast, concentration, texture and space provide lots of illustrations and numerous suggestions for achieving particular effects.

Wucius Wong, Principles of two-dimensional form, New York: Van Nostrand Reinhold, 1988. After describing the aspects of form and how to design a form, the author applies the concepts from his earlier books to the creation of representational forms.