blocks|key|757438|text|分形编程将向您介绍递归、迭代、图形编程概念、图像处理和用户界面设计。从数学的角度来看，你将学习几何，复数，莫比乌斯变换(克莱因分形)，仿射变换(IFS分形)，求根方法(牛顿分形)。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|757439|最重要的是，你会得到奖励，因为你会看到你的努力产生了奇怪和不同寻常的图像。|757440|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|F|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|G|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|H|8|@]|9|@]|A|$]]]|E|$]]

Fractal programming would introduce you to recursion, iteration, graphics programming concepts, image processing, and user interface design. From a mathematics point of view, you would learn about geometry, complex numbers, Mobius transformations (Kleinian fractals), Affine transformation (IFS fractals), root-finding methods (Newton fractals).

And on top of all this, you get the reward of seeing your efforts result in strange and unusual images.

blocks|key|749879|text|根据我的记忆，你会很好地处理递归，如果没有else...maybe的话，还有一点位图级别的编程……|type|unstyled|depth|inlineStyleRanges|entityRanges|data|749880|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

From what I remember you'll get a good handle on recursion if nothing else...maybe a little bitmap level programming as well...

blocks|key|313001|text|如果你是初学者，这样的活动肯定会帮助你提高你的技能。除此之外，根据你设定的分形类型和目标，编程分形可视化可能会给你一些特定的技能或知识，比如：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|313002|使用图形，图像processing;|313003|understanding递归和递归structures;|unordered-list-item|313004|
|313005|optimization+techniques;|313006|313007|low-level程序optimizations;|313008|313009|understanding计算机如何操作(例如，为什么分辨率通常是有限的和浮点精度和误差accumulation);|313010|313011|parallel+programming;|313012|313013|some数学改进和扩展您的范围interest;|313014|313015|understanding各种技术(例如，您可以在PixelBender中code+Mandelbrot+set，这是非常快，因为可以在图形处理器上执行)；更复杂的压缩算法(例如，某种类型的分形着色(例如，您发明了自己的分形集合着色|offset|length|313016|313017|understanding+compression);|313018|313019|creativity+:)|313020|313021|这确实是一个多才多艺、有趣的领域，有很多东西需要探索和学习。我过去经常画分形:)|313022|entityMap|0|LINK|mutability|MUTABLE|url|http://labs.adobe.com/technologies/pixelbender/|1|http://octets.ru/programming/flash-platform/pixel-bender-bystraya-otrisovka-mnozhestv-mandelbrota-i-zhyulia/^0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|P|B|0|11|J|1|0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|1K|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|1L|8|@]|9|@]|A|$]]|$1|D|3|E|5|F|7|1M|8|@]|9|@]|A|$]]|$1|G|3|H|5|6|7|1N|8|@]|9|@]|A|$]]|$1|I|3|J|5|F|7|1O|8|@]|9|@]|A|$]]|$1|K|3|H|5|6|7|1P|8|@]|9|@]|A|$]]|$1|L|3|M|5|F|7|1Q|8|@]|9|@]|A|$]]|$1|N|3|H|5|6|7|1R|8|@]|9|@]|A|$]]|$1|O|3|P|5|F|7|1S|8|@]|9|@]|A|$]]|$1|Q|3|H|5|6|7|1T|8|@]|9|@]|A|$]]|$1|R|3|S|5|F|7|1U|8|@]|9|@]|A|$]]|$1|T|3|H|5|6|7|1V|8|@]|9|@]|A|$]]|$1|U|3|V|5|F|7|1W|8|@]|9|@]|A|$]]|$1|W|3|H|5|6|7|1X|8|@]|9|@]|A|$]]|$1|X|3|Y|5|F|7|1Y|8|@]|9|@$Z|1Z|10|20|1|21]|$Z|22|10|23|1|24]]|A|$]]|$1|11|3|H|5|6|7|25|8|@]|9|@]|A|$]]|$1|12|3|13|5|F|7|26|8|@]|9|@]|A|$]]|$1|14|3|H|5|6|7|27|8|@]|9|@]|A|$]]|$1|15|3|16|5|F|7|28|8|@]|9|@]|A|$]]|$1|17|3|-4|5|6|7|29|8|@]|9|@]|A|$]]|$1|18|3|19|5|6|7|2A|8|@]|9|@]|A|$]]|$1|1A|3|-4|5|6|7|2B|8|@]|9|@]|A|$]]]|1B|$1C|$5|1D|1E|1F|A|$1G|1H]]|1I|$5|1D|1E|1F|A|$1G|1J]]]]

If you are a beginner such activity will surely help you to improve your skills. Apart from that programming fractal visualizations depending on the fractal type and the goal you set may give you some specific skills or knowledge like:

<ul>
<li>working with graphics, image processing;</li>
<li>understanding recursion and recursive
structures;</li>
<li>optimization techniques;</li>
<li>low-level program optimizations;</li>
<li>understanding how computer operates
(e.g. why resolution would be
normally limited -> floating point
precision and error accumulation);</li>
<li>parallel programming;</li>
<li>some mathematical improvement and
extend your range of interest;</li>
<li>understanding various technologies
(e.g. you can <a href="http://octets.ru/programming/flash-platform/pixel-bender-bystraya-otrisovka-mnozhestv-mandelbrota-i-zhyulia/" rel="nofollow noreferrer">code Mandelbrot
set</a> in <a href="http://labs.adobe.com/technologies/pixelbender/" rel="nofollow noreferrer">PixelBender</a> which is
really fast since may be executed on
GPU);</li>
<li>understanding complex compression
algorithms (e.g. some kind of fractal
compression);</li>
<li>creativity (e.g. you invent your own
fractal set coloring algorithm);</li>
<li>much more else :)</li>
</ul>

It is indeed a versatile and interesting field, lots of things to explore and learn. I used to draw fractals a lot :)

blocks|key|4093583|text|分形让我想到了复数和branch-points。我想，这是否是一件好事，这是一个见仁见智的问题。:-)|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|4093584|entityMap|0|LINK|mutability|MUTABLE|url|http://en.wikipedia.org/wiki/Branch_point^0|A|D|0|0^^$0|@$1|2|3|4|5|6|7|L|8|@]|9|@$A|M|B|N|1|O]]|C|$]]|$1|D|3|-4|5|6|7|P|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]]]

Fractals got me thinking about complex numbers and <a href="http://en.wikipedia.org/wiki/Branch_point" rel="nofollow noreferrer">branch-points</a>. Whether that was a good thing is, I suppose, a matter of opinion. :-)

blocks|key|312755|text|任何类型的编程经验都是有用的。所以，是的，它是。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|312756|尤其是对于：|312757|312758|unordered-list-item|312759|+problems|312760|basic+algorithms|312761|，当然还有分形编程|312762|312763|entityMap^0|0|0|0|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|P|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|Q|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|R|8|@]|9|@]|A|$]]|$1|E|3|-4|5|F|7|S|8|@]|9|@]|A|$]]|$1|G|3|H|5|F|7|T|8|@]|9|@]|A|$]]|$1|I|3|J|5|F|7|U|8|@]|9|@]|A|$]]|$1|K|3|L|5|F|7|V|8|@]|9|@]|A|$]]|$1|M|3|-4|5|6|7|W|8|@]|9|@]|A|$]]|$1|N|3|-4|5|6|7|X|8|@]|9|@]|A|$]]]|O|$]]

Any kind of programming experience is useful. So yes it is.

Especially for:

<ul>
<li>math problems</li>
<li>basic algorithms</li>
<li>and of course fractal programming</li>
</ul>

blocks|key|749891|text|它可能会给你实现数学公式的练习。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|749892|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

It'll maybe give you practice in implementing mathematical formulae.

blocks|key|757368|text|一些分形是显式递归的很好的可视化示例；如果您很难理解这个概念，那么它们可能是很好的问题。你可以从“乌龟图形”风格的分形路径开始，比如希尔伯特曲线，或者经典的“雪花”分形。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|757369|许多分形生成方法使用繁重的数字运算(例如，Mandelbrot和Julia集)。当然，数字运算本身就是一个领域，调整您的分形生成器以尽可能快地运行可能是一个很好的优化练习。|757370|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|F|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|G|8|@]|9|@]|A|$]]|$1|D|3|-4|5|6|7|H|8|@]|9|@]|A|$]]]|E|$]]

Some fractals are good visual examples for explicit recursion; if you have a hard time with that concept, they might be good problems to work. You can start with "turtle graphics" style fractal paths like the Hilbert curve, or the classic "snowflake" fractal.

Many fractal-generation methods use heavy-duty number crunching (e.g., Mandelbrot and Julia sets). Number crunching is of course a field in itself, and tweaking your fractal generator to run as fast as possible can be a nice exercise in optimization.

blocks|key|2661972|text|我不认为编程分形会教会你任何特别的东西。根据分形的不同，我想它可能会教你一些数学或分形的知识。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2661973|然而，我确实认为分形作为编程的入门很有趣，初学者/学生通常对结果着迷，无论是更多的图形分形，如mandelbrot或julia+set，还是更容易理解的L系统。|2661974|当然，如果你是编程新手，它也有望教会你很多关于编程的知识。如果没有其他东西，分形看起来很有趣。|2661975|entityMap^0|0|0|0^^$0|@$1|2|3|4|5|6|7|H|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|I|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|J|8|@]|9|@]|A|$]]|$1|F|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|G|$]]

I don't think programming fractals will teach you anything in particular. Depending on the fractal, I suppose it might teach you a bit about math or fractals in general.

However, I do think fractals are fun as an introduction to programming, and beginners/students are often fascinated by the result, be it more graphic fractals like mandelbrot or julia sets, or more easy to understand L-systems.

Of course, if you're new to programming, it'll also hopefully teach you a lot about programming in general. If nothing else, fractals are interesting to look at.

blocks|key|312889|text|当我还是一名大学生的时候，我们使用分形绘图来支持我们的并行处理工作。它的计算很快变得相当密集，因此有多个CPU可用来完成这项工作，这样您就可以看到效率的明显提高。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|312890|因此，除了递归，我想说它有助于学习如何在并行处理器之间平衡CPU负载。|312891|..。或者，如果设备不可用，它可能会教会你禅宗般的耐心。:)|312892|entityMap^0|0|0|0^^$0|@$1|2|3|4|5|6|7|H|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|I|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|J|8|@]|9|@]|A|$]]|$1|F|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|G|$]]

when I was an undergrad, we used fractal drawing to power our work in parellel processing. It gets fairly computationally intensive quickly, so having multiple CPUs available to do the work lets you see a visible increase in efficiency. 

So, along with recursion, I'd say it helps with learning how to balance CPU load across parallel processors. 

... or if the equipment isn't available, it probably teaches you Zen-like patience. :)

blocks|key|4093713|text|好主意！我认为对分形进行编码是一个很好的“学习”规模的程序。它有一些很好的功能:通常你不需要太多的第三方代码，它们可以在相当短的时间内实现(和复杂性)，最后你也会得到一些很好的东西，这也验证了你的工作。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|4093714|此外，在数学和数值算法的实现中都有大量的基本问题，如果你这样做了，你会遇到这些问题。|4093715|从像基本的Mandelbrot集生成器这样简单的东西开始，您可以扩展到评论者提到的所有类型的问题。即使坚持到这一点，你也可以学习优化技术(为什么我的生成器这么慢)和数值问题(为什么我不能在这里放大)，但如果你想了解一点颜色理论(+L_a_b*空间到底是什么)和其他零碎的东西。|4093716|玩得开心!|4093717|entityMap^0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|J|8|@]|9|@]|A|$]]|$1|B|3|C|5|6|7|K|8|@]|9|@]|A|$]]|$1|D|3|E|5|6|7|L|8|@]|9|@]|A|$]]|$1|F|3|G|5|6|7|M|8|@]|9|@]|A|$]]|$1|H|3|-4|5|6|7|N|8|@]|9|@]|A|$]]]|I|$]]

Great idea! I think coding up fractals makes a great "etude" (study) sized program. It has some nice features this way: generally you won't require much 3rd party code, they can be implemented in a reasonably short amount of time (and complexity) and you get something nice too look at in the end which also verifies your work.

Also there are loads of basic issues in both mathematics and the implementation of numerical algorithms that you will bump into if you do this.

From something as simple as a basic Mandelbrot set generator you can branch out into all sorts of issues as commenters have mentioned. Even sticking with just that, though, you can learn about optimization techniques (why is my generator so slow) and numerical issues (why can't I zoom past here), but also if you want to a bit of color theory (what's Lab* space anyway) and other bits and pieces.

Have fun!

blocks|key|2662102|text|分形在智力上是一个非常有趣的话题，即使是最简单的实现也会让你学习到复数数学、图形生成、缩放图像和一般编程。|type|unstyled|depth|inlineStyleRanges|entityRanges|data|2662103|entityMap^0|0^^$0|@$1|2|3|4|5|6|7|D|8|@]|9|@]|A|$]]|$1|B|3|-4|5|6|7|E|8|@]|9|@]|A|$]]]|C|$]]

Fractals is a very intellectually interesting topic and well even the simplest implementation will make you learn about complex number maths,graphics generation,scaling images, and general programming.

Would learning to program fractals help think clearly about certain set of programming problems?

Programming Fractals

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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