这本是讨论分形（Fractal）较为经典的书籍，且同时融合了混沌（Chaos）的思想，通过两种思维模式相互印证，暗示了真实世界中复杂变化的源泉所在。开篇由生活中简单反馈系统所得到的分形图案，引入到各种经典的分形数学模型中，然后根据它们独特的几何性质，讨论了复杂度和维度的定义。第五章开始转向应用的角度来审视分形的特点，其中有对由随机游戏来得到分形图案做了数学的分析，还有帕斯卡三角同分形的联系，和如何利用分形的思维构造真实世界中复杂的随机模型。后面的十和十一章又回到比较偏理论的讨论。大致是通过更改二次迭代式中的参数来逐步得到从简单到完全混沌的反馈系统，也就是经典的 Feigenbaum Diagram，而它具有明显的分形特征。在简单延伸了一下之前的构造方法后，结尾两章详细介绍了 Julia Sets 和 Mandelbrot Set 的定义和绘制技巧。当然，这肯定离不开通过简单规则由计算机绘制的各种美妙图案啦。其实，在理解这个拥有无限细节的图案后，就可以领悟到分形和混沌只是从不同角度观察它得到的结果而已。在只关注一个特殊点时，所得到就是混沌，因为任何小小偏移都会放大到某个细节完全不同的图案中；而只关注一片有限的区域时，所得到的就是分形，因为你总是可以在另外一个层次的细节上找到相同的图案。最后附录部分简单讨论了如何用分形来压缩图像，还有一些理论的框架，作为正文中某些章节的补充。警告，本书可能会对读者的世界观造成强烈冲击——欧几里得的几何世界将会被分形世界所取代。

观点摘录：
Page 111: Now it is intuitively clear that a finite number of points can be covered so that there is no intersection. Curves can be covered so that the order of the cover is 2 and there is no cover of sufficiently small disks or balls with order 1. Surfaces can be covered so that the order of the cover is 3 and there is no cover of sufficiently small disks or balls with order 2. Thus the covering dimension of points is 0, that of curves is 1, and that of surfaces is 2.

Page 159: Fractal geometry offers a totally new and very powerful modelling framework for such encoding problems. In fact, we count speculate that our brain uses fractal-like encoding schemes.

Page 297: Nothing in Nature is random... A thing appears random only through the incompleteness of our knowledge. --Spinoza

Page 401: This feature present in so-called parametric L-systems, is very powerful and helps enormously to create more realistic biological models.

Page 913: When it came to a simple theoretical motivation, we use the sup metric which is very convenient for this. But for practice, we are happier using the rms metric which allows us to make least square computations.

图书信息：

Author	Peitgen, Heinz-Otto, 1945-
Title	Chaos and fractals : new frontiers of science / Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe.
Publisher	New York ; Hong Kong : Springer-Verlag, c1992.

图书目录：

Table of Contents
	Preface
	Authors
	Foreword / Mitchell J. Feigenbaum					1
	Introduction: Causality Principle, Deterministic Laws and Chaos					9
1	The Backbone of Fractals: Feedback and the Iterator					15
2	Classical Fractals and Self-Similarity					63
3	Limits and Self-Similarity					135
4	Length, Area and Dimension: Measuring Complexity and Scaling Properties					183
5	Encoding Images by Simple Transformations					229
6	The Chaos Game: How Randomness Creates Deterministic Shapes					297
7	Recursive Structures: Growing of Fractals and Plants					353
8	Pascal's Triangle: Cellular Automata and Attractors					407
9	Irregular Shapes: Randomness in Fractal Constructions					457
10	Deterministic Chaos: Sensitivity, Mixing, and Periodic Points					507
11	Order and Chaos: Period-Doubling and its Chaotic Mirror					585
12	Strange Attractors: The Locus of Chaos					655
13	Julia Sets: Fractal Basin Boundaries					769
14	The Mandelbrot Set: Ordering the Julia Sets					841
	A A Discussion of Fractal Image Compression / Yuval Fisher					903
	B Multifractal Measures / Carl J. G. Evertsz, Benoit B. Mandelbrot					921
	Bibliography					955
	Index					971

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