Very recent advances in computer technology provide the power of mainframe systems in relatively compact and inexpensive personal computers. Over the next decade this tremendous computing power will become available in high schools throughout the country. This new technological resource will be harnessed as a teaching tool for specific topics in math and science, focusing on random processes in nature and their deep connection to concepts in probability and fractal geometry. Such natural phenomena as the growth of snow flakes via random aggregation and the disordered geometric configurations of polymer chains demonstrate that fundamentally random microscopic processes can give rise to predictable macroscopic behaviors. They also give rise to random fractal structures of inherent interest and great beauty. Because it is impossible to view the underlying processes directly, computer simulation and visualization is an indispensable tool for understanding and studying these phenomena. In the process of "doing science" with both hand-on experiments and computer simulations, students will learn abstract mathematical concepts in a context which is at once concrete and inherently motivating. Futhermore, the techniques they will employ will mirror in most respects those in current use by researchers, thus forging an unprecedented link between this curriculum and the professional worlds of science and mathematics.
