2004, Peitgen, Heinz-Otto, Jürgens, Hartmut, Saupe, Dietmar

Being introduced to the Pascal triangle for the first time, one might think that this mathematical object was a rather innocent one. Surprisingly it has attracted the attention of innumerable scientists and amateur scientists over many centuries. One of the earliest mentions (long before Pascal’s name became associated with it) is in a Chinese document from around 1303.1 Boris A. Bondarenko,2 in his beautiful recently published book, counts several hundred publications which have been devoted to the Pascal triangle and related problems just over the last two hundred years. Prominent mathematicians as well as popular science writers such as Ian Stewart,3 Evgeni B. Dynkin and Wladimir A. Uspenski,4 and Stephen Wolfram5 have devoted articles to the marvelous relationship between elementary number theory and the geometrical patterns found in the Pascal triangle. In chapter 2 we introduced one example: the relation between the Pascal triangle and the Sierpinski gasket.

2004, Peitgen, Heinz-Otto, Jürgens, Hartmut, Saupe, Dietmar

For many, chaos theory already belongs to the greatest achievements in the natural sciences in this century. Indeed, it can be claimed that very few developments in natural science have awakened so much public interest. Here and there, we even hear of changing images of reality or of a revolution in the natural sciences.

2003, Jürgens, Hartmut, Saupe, Dietmar

SCOUT is a program which implements a series of algorithms based on ideas described in chapter 12 concerning PL continuation methods. The problem to be solved numerically is a nonlinear fixed point or eigenvalue problem, i. e. to find the zeros of F:R^N×R→R^N
(x,λ)↦F(x,λ). More precisely, the following is a list of the various problem areas that are handled by SCOUT.