The Mystery of the Butterfly Effect: Closer to Fractals and Chaos

Some people hail fractal and chaos theory as the third revolution in physics in the 20th century after relativity and quantum mechanics. This book first describes the basic knowledge and characteristics of various fractals, including fractals produced by linear iterations such as fractal dragons, families, and curves, as well as Mandelbrot sets, Julia sets, etc. Produced by nonlinear iterations. Through these examples, the concepts of self-similarity and fractal dimension are introduced. Then, following the history of the development of chaos phenomena, readers are brought into the world of magical chaos theory by telling stories and anecdotes such as Poincaré's three-body problem and Lorenz's butterfly effect. Then, through the discussion of a simple chaotic system - logistic map, concepts such as bifurcation theory, stability, and Feigenbaum's universal constant are introduced in detail. The second half of the book introduces the applications and prospects of fractals and chaos in various fields, the relationship between fractals and chaos, and the nonlinear science developed closely related to fractal chaos. As the saying goes: "It is better to teach a man to fish than to teach him to fish." As a popular science book, it is important to introduce knowledge, but it is even more important to teach scientific research methods. This book strives to reflect this purpose. The author not only introduces science, but also painstakingly focuses on the thinking process of scientists when they make major discoveries, leading readers to think together and get profound enlightenment from the experiences and lessons of their predecessors, thereby stimulating readers' curiosity and creativity. A popular science book suitable for all ages and compatible with arts and sciences. With pictures and texts, it uses relaxed and interesting language and popular and vivid illustrations to describe profound and difficult scientific theories. Peeling the nuts of theory for readers, so that people in different fields can appreciate the infinite charm of mathematics and physics.