这是 Springer Verlag 当年差不多同一时期出版的“分形三部曲”佳作之一。另外两本是《The Science of Fractal Images》和《The Beauty of Fractals》。https://www.springer.com/gp/book/9781461283492 https://www.springer.com/gp/book/9783540158516 我觉得还有两本也不错（不过是面向大众科普的）……
This is one of the trio of great books that Springer Verlag produced around the same time. The other two are The Science of Fractal Images and Beauty of Fractals. https://www.springer.com/gp/book/9781461283492 https://www.springer.com/gp/book/9783540158516 Two other books that I think are good (but which are for general audiences) are…
他们引用了 IBM 实验室。《The Beauty of Fractal Images》里提到了一台带扩展精度的 IBM 4361-5，书末附近的一张黑白插页还用了一台 IBM 4250 打印机。而在《The Science of Fractal Images》里，彩页致谢列出了以下人物和机构：http://imgur.com/a/KSnDZ
They reference IBM labs. The Beauty of Fractal Images talks about an IBM 4361-5 with extended precision, and an IBM 4250 printer for one of the monochrome plates near the end of the book. The Science of Fractal Images lists, as credits for the colour plates, these people and institutions: http://imgur.com/a/KSnDZ
……看看它们到底怎么样。《The Beauty of Fractals》包含很多彩色插页，上面的图像在 1986 年绝对称得上惊艳。每一页都有大量数学公式。（塞进去的数学内容确实多得要命）。《The Science of Fractal Images》篇幅稍长一些，彩页比较少，数学推导稍微少一点（或者可能只是排得更分散？），并且有一些算法的伪代码描述。另外两本就轻松易读得多了。……
…check what they're like. The Beauty of Fractals contains a lot of colour plates with images that were remarkable for 1986. There's plenty of math on every page. (It really crams a lot of math in). The Science of Fractal Images is a bit longer. It has fewer colour plates. There's a bit less math (or maybe it's just spread out a bit more?) and there are some pseudo-code descriptions of algorithms. The other two are much lighter.…
Loved the discussion of distance estimator formulae. As I recall them, to derive one of the results in The Science of Fractal Images you'd need to use Koebe's 1/4th theorem applied to the potential function (or a related function which is analytic) and thus you'd solve the factor problem. It's a little hazy, since I did this 6 years…
中点位移法（Midpoint displacement）在《The Science of Fractal Images》（以及《The Beauty of Fractal Images》）里都有提及，曼德博的那本《Fractal Geometry of Nature》里也有。手机拍的，传颠倒了抱歉：http://m.imgur.com/JGCpnIu 《Science of Fractal Images》里的一个片段
Midpoint displacement is mentioned in The Science of Fractal Images (and the Beauty of Fractal Images), and also in Mandelbrot's book Fractal Geometry of Nature. From a phone, sorry about upside down: http://m.imgur.com/JGCpnIu A snippet from "Science of Fractal Images"
这是 Springer Verlag 当年差不多同一时期出版的“分形三部曲”佳作之一。另外两本是《The Science of Fractal Images》和《The Beauty of Fractals》。https://www.springer.com/gp/book/9781461283492 https://www.springer.com/gp/book/9783540158516 我觉得还有两本也不错（不过是面向大众科普的）……
This is one of the trio of great books that Springer Verlag produced around the same time. The other two are The Science of Fractal Images and Beauty of Fractals. https://www.springer.com/gp/book/9781461283492 https://www.springer.com/gp/book/9783540158516 Two other books that I think are good (but which are for general audiences) are…
他们引用了 IBM 实验室。《The Beauty of Fractal Images》里提到了一台带扩展精度的 IBM 4361-5，书末附近的一张黑白插页还用了一台 IBM 4250 打印机。而在《The Science of Fractal Images》里，彩页致谢列出了以下人物和机构：http://imgur.com/a/KSnDZ
They reference IBM labs. The Beauty of Fractal Images talks about an IBM 4361-5 with extended precision, and an IBM 4250 printer for one of the monochrome plates near the end of the book. The Science of Fractal Images lists, as credits for the colour plates, these people and institutions: http://imgur.com/a/KSnDZ
……看看它们到底怎么样。《The Beauty of Fractals》包含很多彩色插页，上面的图像在 1986 年绝对称得上惊艳。每一页都有大量数学公式。（塞进去的数学内容确实多得要命）。《The Science of Fractal Images》篇幅稍长一些，彩页比较少，数学推导稍微少一点（或者可能只是排得更分散？），并且有一些算法的伪代码描述。另外两本就轻松易读得多了。……
…check what they're like. The Beauty of Fractals contains a lot of colour plates with images that were remarkable for 1986. There's plenty of math on every page. (It really crams a lot of math in). The Science of Fractal Images is a bit longer. It has fewer colour plates. There's a bit less math (or maybe it's just spread out a bit more?) and there are some pseudo-code descriptions of algorithms. The other two are much lighter.…
很喜欢关于距离估计公式（distance estimator formulae）的讨论。依稀记得，要推导出《The Science of Fractal Images》里的一个结果，需要把柯贝 1/4 定理（Koebe's 1/4th theorem）应用到势函数（或者某个相关的解析函数）上，从而解决因子问题。记忆有点模糊了，毕竟我是 6 年前搞的……
Loved the discussion of distance estimator formulae. As I recall them, to derive one of the results in The Science of Fractal Images you'd need to use Koebe's 1/4th theorem applied to the potential function (or a related function which is analytic) and thus you'd solve the factor problem. It's a little hazy, since I did this 6 years…
中点位移法（Midpoint displacement）在《The Science of Fractal Images》（以及《The Beauty of Fractal Images》）里都有提及，曼德博的那本《Fractal Geometry of Nature》里也有。手机拍的，传颠倒了抱歉：http://m.imgur.com/JGCpnIu 《Science of Fractal Images》里的一个片段
Midpoint displacement is mentioned in The Science of Fractal Images (and the Beauty of Fractal Images), and also in Mandelbrot's book Fractal Geometry of Nature. From a phone, sorry about upside down: http://m.imgur.com/JGCpnIu A snippet from "Science of Fractal Images"