TY  - BOOK
AU  - Mumford,David
AU  - Series,Caroline
AU  - Wright,David James
TI  - Indra's pearls: the vision of Felix Klein 
SN  - 0521352533 
U1  - 514.742 MUM 
PY  - 2002///
CY  - United Kingdom, New York
PB  - Cambridge University Press
KW  - Klein, Felix, -- 1849-1925
KW  - Geometry.
KW  -  Symmetry
N1  - Include index
N2  - "Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple co-existing symmetries, each simple in itself, but whose interactions produce fractals on the edge of chaos. For a century these images, which were practically impossible to draw by hand, barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in so doing found further extraordinary images of their own. Join the authors on the path from some basic mathemathical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can learn to understand what the images mean and follow the step-by-step instructions for writing computer programs that generate them. More advanced readers can see how the images relate to ideas that take them to the forefront of research
ER  -