Today the ‘theory of complex dynamical systems’ is often referred to as a revolution, illuminating all of science. Computer-graphical methods and experiments today define the methodology of a new branch of mathematics: ‘experimental mathematics’. Its content is above all the theory of complex dynamical systems. ‘Experimental’ here refers primarily to computers and computer graphics. In contrast to the experiments are ‘mathematical cross-connections’, analysed with the aid of computers, whose examples were discovered using computer-graphical methods. The mysterious structure of these computer graphics conceals secrets which still remain unknown, and lie at the frontiers of thought in several areas of science. If what we now know amounts to a revolution, then we must expect further revolutions to occur.

• The groundwork must therefore be prepared, and

• people must be found who can communicate the new knowledge.

We believe that the current favourable research situation has been created by the growing power and cheapness of computers. More and more they are being used as research tools. But science's achievement has always been to do what can be done. Here we should mention the name of Benoi§t B. Mandelbrot, a scientific outsider who worked for many years to develop the fundamental mathematical concept of a fractal and to bring it to life.

Other research teams have developed special graphical techniques. At the University of Bremen fruitful interaction of mathematicians and physicists has led to results which have been presented to a wide public. In this context the unprecedented popular writings of the group working under Professors Heinz-Otto Peitgen and Peter H. Richter must be mentioned.