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楼主: G-Spider

[欣赏] 分形之美

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发表于 2011-8-28 09:37:03 | 显示全部楼层
1# G-Spider
请教楼主有三维Hillbert曲线的的分型实现代码吗?自己弄了半天没成功
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2011-10-21 13:12:28 | 显示全部楼层
Fractal分形源码一枚:
FractalExplorer64.zip (237.81 KB, 下载次数: 5)
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2011-10-21 13:25:31 | 显示全部楼层
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2012-2-1 18:21:26 | 显示全部楼层
很美,就是有大图吗?想作为桌面啊
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2012-2-11 22:04:10 | 显示全部楼层
以前也编过,不过没这么漂亮
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2013-4-2 22:24:23 | 显示全部楼层
Mandelbulb (3d mandelbrot)
Introduction :
http://www.skytopia.com/project/fractal/mandelbulb.html

Math formula :
http://www.skytopia.com/project/fractal/2mandelbulb.html

To see the beast :
http://www.fractalforums.com/3d- ... uality-mandelbulbs/
  1. What's the formula of this thing?

  2. There are a few subtle variations, which mostly end up producing the same kind of incredible detail. Listed below is one version. Similar to the original 2D Mandelbrot, the 3D formula is defined by:

  3. z -> z^n + c

  4. ...but where 'z' and 'c' are hypercomplex ('triplex') numbers, representing Cartesian x, y, and z coordinates. The exponentiation term can be defined by:

  5. {x,y,z}^n = r^n { sin(theta*n) * cos(phi*n) , sin(theta*n) * sin(phi*n) , cos(theta*n) }
  6. ...where:
  7. r = sqrt(x^2 + y^2 + z^2)
  8. theta = atan2( sqrt(x^2+y^2), z )
  9. phi = atan2(y,x)

  10. And the addition term in z -> z^n + c is similar to standard complex addition, and is simply defined by:

  11. {x,y,z}+{a,b,c} = {x+a, y+b, z+c}

  12. The rest of the algorithm is similar to the 2D Mandelbrot!

  13. Here is some pseudo code of the above:

  14. r = sqrt(x*x + y*y + z*z )
  15. theta = atan2(sqrt(x*x + y*y) , z)
  16. phi = atan2(y,x)

  17. newx = r^n * sin(theta*n) * cos(phi*n)
  18. newy = r^n * sin(theta*n) * sin(phi*n)
  19. newz = r^n * cos(theta*n)

  20. ...where n is the order of the 3D Mandelbulb. Use n=8 to find the exact object in this article.
复制代码
http://sourceforge.net/projects/mandelbulber/
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2013-4-3 14:42:41 | 显示全部楼层
用Mathematica做的动态放大Mandelbrot set,


另一种配色:
mymma.googlecode.com/files/mandel_jet.gif
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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