Polar Sun

QuoteFOREWARD

This work follows and largely replaces my 1977 Essay, FRACTALS: FORM, CHANCE AND DIMENSION, which had followed and largely replaced my 1975 Essay in French, LES OBJETS FRACTALS: FORME, HASARD ET DIMENSION. Each stage involved new art, a few deletions, extensive rewriting that affected nearly every section, additions devoted to my older work, and - most important - extensive additions devoted to new developments.

Richard F. Voss made an essential contribution to the 1977 Essay and to this work, especially by designing and now redesigning the fractal flakes, most landscapes, and the planets. The programs for many striking illustrations new to this Essay are by V. Alan Norton.

Other invaluable, close, long-term associates were Sigmund W. Handelman, then Mark R. Laff, for computation and graphics, and H. Catharine Dietrich, then Janis T. Riznychok, for editing and typing.

Individual acknowledgments for the programs behind the illustrations and for other specific assistance are found after the list of references at the end of the volume.

For their backing of my research and my books, I am deeply indebted to the Thomas J. Watson Research Center of the International Business Machines Corporation. As Group Manager, Department Director, and now Director of Research, IBM Vice President Ralph E. Gomory imagined ways of sheltering and underwriting my work when it was a gamble, and now of giving it all the support I could use.

My first scientific publication came out on April 30, 1951. Over the years, it had seemed to many that each of my investigations was aimed in a different direction. But this apparent disorder was misleading: it hid a strong unity of purpose, which the present Essay, like its two predecessors, is intended to reveal. Against odds, most of my works turn out to have been the birth pangs of a new scientific discipline.