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1·Both vegetables and quadratic polynomials are made more interesting with the Mandelbrot set.

有了曼德尔勃特集合，蔬菜和二次多项式都变得有趣多了。

2·Graphic designers have lots of fun with the Mandelbrot set. There are several fractal geometry software programs available for download.

曼德尔勃特集合给图像设计师带来了许多乐趣。这里有几个可供下载的分形几何软件。

3·The Mandelbrot set, which is most commonly represented by the above illustration, provides a way of understanding roughness in the world around us.

上图是曼德布·洛特集最常见的表现形式，它给我们提供了一种理解周围世界的粗糙程度的方式。

4·For instance, I've seen this come up in Mandelbrot set explorers where you can zoom in so far that the entire graph falls between the nearest two doubles.

例如，我曾经在Mandelbrot集合管理器看见过这种情况。在其中可以放大曲线图，让其落在最近的两个双精度数之间。

5·The Mandelbrot set is infinitely deep and complex at all scales, but a float or a double can go only so deep before losing the ability to distinguish adjacent points.

Mandelbrot集合在各个级别上都是非常细微和复杂的，但是float或double可以在失去区分相邻点的能力之前达到这个细微的级别。

6·Both vegetables and quadratic polynomials are made more interesting with the Mandelbrot set. The formula explains the repeating complexity of broccoli heads like this one.

有了曼德尔勃特集合，蔬菜和二次多项式都变得有趣多了。这个方程序表现了类似图中的花椰菜菜籽的重复的复杂性。

7·This graph shows correspondence between the Mandelbrot set and the logistic map, which explains how complex, chaotic behavior can arise from simple non-linear dynamical equations.

这幅图片展示了曼德尔勃特集合(Mandelbrot set)与离散混沌动力系统(logistic map)之间的一致性，这解释了复杂而无序的行为可以由简单的非线性动态方程序中得出。