xiaongxp

100# lnszdzg
      在几何画板中，可通过设置动态迭代次数来提速，即在需要精细扫描的地方使用大迭代次数，其余地方设为较小的迭代次数。

lnszdzg

Mathcad中，放大倒不是太难，但中心的选择比较难

lnszdzg

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2014-7-9 10:21

lnszdzg

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2014-7-9 10:21

lnszdzg

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2014-7-9 10:22

xiaongxp

Mathcad中，放大倒不是太难，但中心的选择比较难
lnszdzg 发表于 2014-5-31 20:00

定位中心一般选择在边界分枝尖点、边界分枝连接点、螺旋中心。这些点在M集中叫Misiurewicz点，它附近必有一个小M集（数学家谭蕾证明了围绕小M集的边界分枝交点列的维数，当n→∞时以2为极限）。

lnszdzg

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2014-7-9 10:23

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2014-7-9 10:23

lnszdzg

六切圆

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2014-7-9 10:24

lnszdzg

UF代码及效果
6Circles {
init:
  int iter = 0
  float num = 5
  float Xabs = 0
  float Yabs = 0
  float Dsgd0 = 0
  float Dsgd1 = 0
  float Circle = 0
  float ZtoPsqd = 0
  float Rc = @r
  float Phi = #pi /6
  float Rm = Rc * sin(Phi)
  float RcSqd = Rm^2
  bool Trapped = false
loop:
  iter = iter + 1
  if iter > @skip && !Trapped
    Xabs = abs(real(#z))
    Yabs = abs(imag(#z))
    Dsgd0 = (Xabs-Rc*sin(phi))^2 + (Yabs - Rc*cos(phi))^2
    Dsgd1 = (Xabs-Rc*sin(3*phi))^2 + (Yabs - Rc*cos(3*phi))^2
    if Dsgd0 < RcSqd
      Trapped = true
      ZtoPsqd= Dsgd0
        Circle = iter
    elseif Dsgd1 < RcSqd
      Trapped = true
      ZtoPsqd= Dsgd1
        Circle = iter
   endif
endif
final:
  if !trapped
    #solid = true
  else
    Circle = ((Circle + @off) % num)/(num-1)
    float Ratio = sqrt(ZtoPsqd/Rcsqd)
    float ColorIndex = 110 * Ratio + Circle * 140
    #index = (ColorIndex + 1) % 256 /256
  endif
default:
  title = "6 Circles"
  param r
    caption = "Circle radius"
    default = 0.4
  endparam
  param skip
    caption = "Iters to skip"
    default = 0
    hint = "Iterations to skip."
  endparam
  param off
    caption = "Hue cycle"
    default = 0
    min = 0
    max = 7
    hint = "This rotates the coloring order of the balls."
  endparam
}

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2014-7-9 10:24

lnszdzg

七切圆陷阱
7Circles {
init:
  int iter = 0
  float num = 5
  float Xabs = 0
  float Yabs = 0
  float Dsgd0 = 0
  float Dsgd1 = 0
  float Dsgd2 = 0
  float Circle = 0
  float ZtoPsqd = 0
  float Rc = @r
  int n1 = @n
  float Phi = #pi /n1
  float Rm = Rc * sin(Phi)
  float RcSqd = Rm^2
  bool Trapped = false
loop:
  iter = iter + 1
  if iter > @skip && !Trapped
    Xabs = abs(real(#z))
    Yabs = abs(imag(#z))
    Dsgd0 = (Xabs-Rc*sin(phi))^2 + (Yabs - Rc*cos(phi))^2
    Dsgd1 = (Xabs-Rc*sin(3*phi))^2 + (Yabs - Rc*cos(3*phi))^2
    Dsgd2 = (Xabs-0)^2 + (Yabs - 0)^2
    if Dsgd0 < RcSqd
      Trapped = true
      ZtoPsqd= Dsgd0
        Circle = iter
    elseif Dsgd1 < RcSqd
      Trapped = true
      ZtoPsqd= Dsgd1
        Circle = iter
    elseif Dsgd2 < RcSqd
      Trapped = true
      ZtoPsqd = Dsgd2
        Circle = iter
   endif
endif
final:
  if !trapped
    #solid = true
  else
    Circle = ((Circle + @off) % num)/(num-1)
    float Ratio = sqrt(ZtoPsqd/Rcsqd)
    float ColorIndex = 110 * Ratio + Circle * 140
    #index = (ColorIndex + 1) % 256 /256
  endif
default:
  title = "7 Circles"
  param r
    caption = "Circle radius"
    default = 0.18
  endparam
  param n
    caption = "Circle numbers"
    default = 6
    min = 4
    max = 9
  endparam
  param skip
    caption = "Iters to skip"
    default = 0
    hint = "Iterations to skip."
  endparam
  param off
    caption = "Hue cycle"
    default = 1
    min = 0
    max = 7
    hint = "This rotates the coloring order of the balls."
  endparam
}

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2014-7-9 10:25