火焰分形坐标系
我一直在对火焰分形进行一些研究，准备创建自己的火焰分形生成器。我只有一个问题：火焰分形算法使用什么坐标系？
它是像复数曼德尔布罗特集，还是实数系统？ 另外，绘制火焰分形图的最佳范围是多少（即曼德尔布罗特使用（x→-2到2），（y→-2i到2i））？
有关火焰分形的原创文章 (22Mb PDF)
I have been doing some research on flame fractals in preparation of creating my own flame fractal generator. I just have one question: What coordinate system is used in the flame fractal algorithm?
Is it like the Mandelbrot Set with complex numbers, or is it a real number system?
Additionally, what is an optimal range to graph the flame fractals within (i.e. Mandelbrot uses (x-> -2 to 2),(y-> -2i to 2i))?
Original Article about flame fractals (22Mb PDF)
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Apophys、flam3 和其他实现中的坐标系使用 (x,y) 或 (x,y,z)。
如果它有 3d hack。然而，某些变体将 (x,y) 解释为复数，例如莫比乌斯变体或朱莉娅变体。
数学计算的具体细节很难理解，没有人真正知道，
因为现有的代码非常古老，并且已经被很多人开发过。
例如，我遇到过一些与 y 坐标行为异常相关的问题。
编辑：啊，Apophys 和 Flam3 使用某种相机功能，它具有中心点、旋转和放大倍数。中心点是将映射到屏幕中间的点，其余的，您将能够弄清楚。
我实际上是在 Java 实现上进行编码，可以在这里找到： http://sourceforge.net /p/flamethyst/home/Home/
浏览代码以获取有关相机、坐标等的详细信息。
The coordinate system in Apophysis, flam3, and other implementations use (x,y), or (x,y,z).
if it has 3d hack. However, some variations interpret (x,y) as if it was a complex number, for example, the mobius variation, or the julia variation.
The exact details on how the math is done is hard to understand, nobody really knows,
since the existing code is very old, and has been developed by many people.
I have, for example, experienced some problems related to the y coordinate behaving strangely.
EDIT: Ah, Apophysis and flam3 uses sort of a camera function, which has a center point, rotation, and magnification. The center point is what will be mapped to the middle of the screen, and the rest, you'll be able to figure out.
I am actually coding on a Java implementation, which can be found here: http://sourceforge.net/p/flamethyst/home/Home/
Browse the code for details on camera, coordinates, etc.
为了回答您的具体问题，我认为源代码中的错误导致 y 坐标在其中一个变换中翻转，使得负 y 轴向上延伸，正 y 轴向下延伸。
为了回答你的实际问题，即在哪里可以找到有关 apophys 代码库的可怕混乱的信息，互联网上的秘密地方是 deviantart 聊天室，大多数专家了解 apophys 的实际工作原理，网址为 chat.deviantart.com/chat/aposhack 。它要求您注册一个 deviantart 帐户。在聊天中，有几个被标记为“巫师”的人，他们要么使用源代码，厌倦了源代码并正在编写自己的火焰生成器，要么是 Chaotica，这是一个分形火焰渲染器，没有许多错误和数学问题。
如果您仍在研究火焰发生器，我邀请您过来和我们谈论分形。
To answer your specific question, I believe that an error in the source code caused the y coordinate to flipped in one of the transforms so that the negative y axis extends upward and the positive y axis extends downward.
To answer your actual question about where to find information about the aweful mess that is the apophysis codebase, the secret place on the internet where most of the experts in how apophysis actually works is a deviantart chatroom at chat.deviantart.com/chat/aposhack. It requires that you sign up for a deviantart account. In the chat, there are several people labeled 'wizards' who either work with the source code, have gotten sick of the source code and are writing their own flame generators, or are Thomas Ludwig, creator of Chaotica, which is a fractal flame renderer that does not have many of the bugs and mathematical issues as apophysis.
If you are still working on a flame generator, I invite you to stop by and talk fractals with us.