Spiral symmetry

A. Lakhtakia, in H. Istvan and C. A. Pickover (Eds.), Spiral Symmetry, World Scientific, Singapore, 1992. 

Whereas helical symmetry is characterized by a constant amount of translation accompanied by a constant amount of rotation, in spiral symmetry the amounts of translation and rotation change gradually and regularly. D Arcy Thompson capitalized this word in his description,. . a Spiral is a curve which, starting from a point of origin,... 

For those of you interested in other strange map projections, the book Spiral Symmetry has figures showing the Earth transformed to snail-like spirals, doughnuts, cubes, and dodecahedrons. My favorite, the map of the Earth warped to a spiral snail shell, was computed by Agnes Denes, a New York artist. She has also mapped the world to lemons (prolate ovoids) and hot-dog shapes. For further information, see Haigittai and Pickover, Spiral Symmetry ... 

C. Hargittai and C. Pickover, Spiral Symmetry (River Edge, NJ World Scientific, 1992). 

Pickover is currently an associate editor for the scientific journals Computers and Graphics and Computers in Physics, and is an editorial board member for Speculations in Science and Technology, Idealistic Studies, Leonardo, and YLEM. He has been a guest editor for several scientific journals. He is editor of The Pattern Book Fractals, Art, and Nature (World Scientific, 1995), Visions of the Future Art, Technology, and Computing in the Next Century (St. Martin s, 1993), and Visualizing Biological Information (World Scientific, 1995) and coeditor of the books Spiral Symmetry (World Scientific, 1992) and Frontiers in Scientific Visualization (Wiley, 1994). Dr. Pickover s primary interest is in scientific visualization. 

Let us start with the helical spiral symmetry that our Galaxy exhibits in the Domain of Symmetry. It is interesting to note that both these structures, that is, the Galaxy and DNA show the helical structures. Now within these limits let us examine the symmetry present and we first start with the symmetry present in living bodies. 

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