the SUMMER of MY LIFE: Chaos, Fractals, and Mathematics Unpredictability

In the summer I finished school, I discovered a universe.In Tirrenia, July 1985, a teenager with a new computer, a heavy voltage converter, and a book of impossible shapes writes a program in BASIC and presses RUN. Then he goes to the beach. The next morning a shape is waiting on the screen that nobody drew - and it changes the course of his life.It begins as a memoir and becomes a field guide. The Summer of My Life is a journey through chaos, fractals, and the patterns that keep turning up in nature - from the Mandelbrot set to Lorenz's weather, from strange attractors to the edge of what can be predicted at all - and through what it takes to show that one of those patterns is really there.Every figure was generated by code. Every number was computed. Every claim is examined - including the famous ones, and several that do not survive.Thirty-nine chapters take the subject from a single equation to the open problems of the present day: period doubling and Feigenbaum's constant, Lyapunov exponents and the prediction horizon, strange attractors, fractal dimension, Julia and Mandelbrot sets, flows and bifurcations, chaos control and synchronisation, symbolic dynamics, invariant measures, entropy, and multifractals.Nothing is watered down and nothing is taken on trust. Where a claim is proved, it says so. Where it is only measured, it says that too. Where a famous result does not hold up, the book explains why - and applies the same standard to itself.Seventy-eight figures, every one generated from code written for this book, with the parameters printed so any of them can be rebuilt from scratch. Five appendices, including the calculus you need built from nothing, a notation guide, and full sources.Thirty-nine chapters. Seventy-eight figures. One rule, written down correctly, and the patience to wait.