如果您定期关注此博客，您会知道我喜欢分形。我最近在新罕布什尔州纳舒厄度过了一个愉快的下午，我的女儿特雷莎（Teresa）在那儿向我介绍了分形艺术家和计算机极客的格雷戈里·塞尔（Gregory Searle）。这是他的徽标。

Contents

Fractal Generator

格雷格的网页是>。There is much to explore. To get started, click on "Fractal Generator" in the menu on the left of the page, and then on the "Fractal Generator" icon in the center of the next page. Or go directly to>。

You will find yourself in an app, written in JavaScript and running in your browser, where you can endlessly explore the Mandelbrot set and an unlimited collection of variations. You can zoom, pan, change iterators, vary parameters, and select from almost two dozen themes or color maps. You can edit the colormaps and investigate smoothers, renderers, and other effects.

这是格雷格（Greg）用来生产艺术的工具。他写道：“画家使用油漆；我使用CPU。我正在让您使用我的油漆！请注意，这始终是一项正在进行的工作。它将在一时兴起。”

There is a lot of fractal art on the Web. This tool allows you to create your own.

Double Double

通过接近$ 2^{53} $的因素缩放曼德布罗特或类似分形，达到了IEEE双精度浮点的极限。因此，格雷格的发电机切换到双倍精确。这使分数长度翻了一番，并大大减慢了渲染。它不会增加指数，但是这些计算需要更精确，而不是更多的范围。（看https://blogs.mathworks.com/cleve/2017/05/22/quadruple-precision-128-bit-floating-point-arithmetic）

含水层

Greg uses his generator, and his skill, to create unique single-edition prints. To preserve their value, he does not reveal the parameters and never reprints. He displays his work at galleries and exhibitions around New England. Some of it is shown, and offered for sale, on his web site.

Here is a sample.

含水层

两栖动物

两栖动物

Clematis

Clematis

小波

Here is one of his wallpapers, digital images that are available as a free download for use as a desktop background or device lock screen.

小波

mandelbar

Greg did not make the next two images -- I did, using his generator and nonstandard iterators. The color themes and shading are novel. This one is known on the Internet as the "Mandelbar" set because the iterator uses the complex conjugate, with a bar over the $z$,

$$z = \bar{z}^2 + c$$

而不是传统

$$ z = z^2 + c $$

mandelbar

Burning Ship

And this amazing fractal, known as the "Burning Ship", is produced by zooming in on an iterator involving the complex absolute value.

$$ z = | z |^2 + c $$

Burning Ship

To see much more of the Burning Ship fractal, check out this video,https://www.youtube.com/watch?v=CD9yNFmb2FE.

获取MATLAB代码

与Matlab®R2018A一起出版