Color and Symmetry by Arthur L. Loeb (review)

Books 361 nearby text results in smooth development of complicated concepts. The first third of the text considers experiments that demonstrate our response to light. In this context, the physics of light and optics, the nature of the retina and the receptor cells, and the excitation of the nervous system are discussed. This leads to four chapters on color vision, which offer excellent operational definitions for colour matching and discernment. In the sections on brightness and temporal properties, the concept of transfer functions is lucidly introduced and its considerable predictive power demonstrated. The concluding chapters just touch on general properties of perception and models where inhibition plays a significant role. Another whole book would have to be written to cover the topics of motion and depth perception that are completely omitted. The author suggests that their experimental base is not secure and that speculations about them are generally unfounded. Many other omissions are not so easily understood. I should have preferred a better introduction to the concept of quanta, since it is used so extensively. Also in such a physiological approach I should have expected the often used unit of ‘troland’ to be defined, so that its special nature as a corrected measure of flux incident on the retina would be understood. Since there is a discussion of brightness , I wonder at the total omission of the ‘retinex theory’, as explored over the past ten years by E. H. Land [I]. Somehow the excellent work of Yarbus [2] on eye movements was also ignored and would have supported numerous speculations that appear later in the book. A controversy ignored in the text is the assertion by S. S. Stevens [3] that sensory stimulus results in a power function response, not the logarithmic relation used throughout the text, although the differences are to some degree subtle in the context used. Both the bibliography and suggested readings omit the areas of vision research I mentioned above. Cornsweet has considered visual perception in a systematic way, so that reasonably prepared university students can teach themselves by reading the text. It is not a reference work, as the text is tightly interdependent. As an approach to modern concepts involving transfer functions, this is an excellent source. Since the author’s particular view of perception differs somewhat from most, one should look elsewhere for discussions of many topics not covered in this introduction to selected fundamental concepts. REFERENCES 1. E. H.Land and J. J. McCann, Lightness and Retinex Theory, J. Opt. SOC. Am., 61, 1 (Jan. 1971). 2. A. L. Yarbus, Eye Movements and Vision (New York: PlenumPress, 1967). 3. S. S. Stevens,The Psychophysicsof Sensory Function ,in Sensory Communication(Cambridge,Mass.: M.I.T. Press, 1961)p. 1. Color and Symmetry. Arthur L. Loeb. John Wiley and Sons, Chichester, England, 1971. 180 pp., illus. E7.00. Review by: Michael Holt* Anyone who has tried to get to grips with the arcane concepts of symmetry and failed may find a new door opened by this book. It is one of those books that needs, and on the whole repays, as much patience as you can spare-whether you are a crystallographer-mathematician or artist-designer. Starting from Delft tiles, Loeb builds up the 17 classical plane symmetry patterns not analytically, as is the standard practice, but synthetically. This is only the first of his departures from routine symmetry theory; central to his theory is the idea of a centre of rotation, which he dubs a rotocentre. A design may have a repeat pattern with several rotocentres that are constrained among themselves, Loeb shows, by a deceptively simple Diophantine equation that encapsulates the ground rules for building up allowable patterns-mosaics, wallpaper patterns, crystal structures or whatever. The book embraces, quite extensively, mirror symmetry (enantiomorphy) or ‘flopped’ patterns as designers would say. The ground well prepared, the author springs his second surprise, the raisoii d’&tre of the book: a complete breakaway from crystallographic orthodoxy as enshrined in Shubnikov’s classic treatment. He treats motifs as methematically distinct when they are differently coloured. (Coloured motifs are normally treated as all ‘grey’.) Like MacGillavry, Loeb discerns in Maurits Escher’s ‘Black and White Knights’ a mathematical operation relating...