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The study of basic fractal geometry can help build students' enthusiasm for learning early in their undergraduate careers. To most undergraduate students, fractals are new, visually appealing, useful, and mathematically accessible. As a result, fractals can be an effective vehicle for introducing and reinforcing multiple modes of learning, which at many institutions is one of the main goals of general first-year undergraduate education. This article describes how fractals are used in one institution's "Freshman Seminar" program to help accomplish these goals.

This brief article is directed towards young readers, perhaps in their teens, who might be thinking about their future careers and the paths that they might like to follow in later life. I give them for consideration an outline of the fun and excitement that I have myself experienced in scientific research, and encourage them to follow me. To do this, I start by giving some remarks about my own early life and its choices. I then identify some of the decisions and lucky breaks that led to my main scientific work on the theories of stability, nonlinear dynamics and chaos. I point to some new frontiers where knowledge of the physical sciences is spreading into wider areas such as the bio-mechanics of DNA and the prediction of tipping points that could dramatically increase global warming. Finally I give some detailed advice that could be useful as you hopefully enter the thrilling world of scientific research.