Mandelbrot, who did the experiment with stock exchanges prices, for example, noted that although the outcomes were variable, there were, in fact, certain constancy.
例如，做过股票交易所价格实验的曼德尔布洛特指出，尽管结果是可变的，但实际上存在一定的一致性。
One of my own demos: Bouncing Mandelbrot Cubes.
我的一个演示：弹跳曼德尔·布罗立方体。
The fractal sequence and Mandelbrot-Julia sets of generalized Gauss sums are studied.
研究了广义高斯和的分形序列及其M-J集。
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。
The complexities that Mandelbrot observed would ultimately be used to understand more than mathematical objects.
曼德布·洛特观察到的复杂性最终会被用于理解除数学对象以外的其他对象。
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。
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。
Mandelbrot says he spent the next two years groping, exploring first one field and then another, without any clear sense of the connecting thread.
曼德布洛特说在随后的的两年里他在多个领域中摸索，却没有明显的相联系的线索。
These two methods were extended, and a series of internal structure images of the general Mandelbrot sets for negative real index number were given out.
文中将这两种方法进行了推广，给出了一系列负实数阶广义M集的内部结构图。
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。
The pioneering chaos theorist Benoit Mandelbrot found that annual flood levels of the Nile follow this pattern; others have observed it in music and air turbulence.
混沌理论先驱BenoitMandelbrot发现尼罗河每年的洪水泛滥程度符合这个性质，音乐和空气湍流中也有这个性质。
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。
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。
The mathematician Benoit Mandelbrot, who pioneered the application of chaos theory to financial markets, refers to this phenomenon as the "multifractal nature of trading time."
伯尼特·曼德尔布罗特是数学家，他首先把混沌理论运用到金融市场，他说这种现象是交易时间的不规则性。
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(Mandelbrotset)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。
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(Mandelbrotset)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。
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