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18# xiaongxp
知道了,向老师,表示理解。由于地域遥隔,不能帮忙,深感为憾。望向老师保重,顺祝中秋快乐,万事如意!
21# 柳烟
谢谢柳老师。
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CubicRoots-Mandel.gsp (21.62 KB)
Cayley-jul {
; Ron Barnett, February 1999
; based upon the formula of Mark Townsend
init:
  complex fz = 0
  complex fzp = 0
  complex fzp2 = 0  
  #z = #pixel
  oldz = 0
  a = @p1
  float iterate = 0
loop:
  iterate = iterate + 1
  oldz = #z
  fz = #z^3 - a*z - a + 1
  fzp = 3*#z^2 - a
  fzp2 = 6*#z
  if @converge == 0                          ; Newton
    #z = #z - fz/fzp
  elseif @converge == 1                      ; Householder
    #z = #z - fz/fzp*(1 + fz*fzp2/(2*fzp^2))   
  elseif @converge == 2                      ; Halley
    #z = #z - 2*fz*fzp/(2*fzp^2 - fz*fzp2)  
  elseif @converge == 3                      ; Schroder
    #z = #z - fz*fzp/(fzp^2 - fz*fzp2)  
  elseif @converge == 4                      ; Ho custom
    #z = #z - fz/fzp*(1 + fz*fzp2/(@custom*fzp^2))      
  elseif @converge == 5                      ; Ha custom
    #z = #z - 2*fz*fzp/(@custom*fzp^2 - fz*fzp2)  
  elseif @converge == 6                      ; H_S custom
    #z = #z - @custom*fz*fzp/(@custom*fzp^2 - fz*fzp2)      
  elseif @converge == 7                      ; Mixed1
    if  iterate % 2 == 0
      #z = #z - fz/fzp*(1 + fz*fzp2/(2*fzp^2))  
    else
      #z = #z - fz/fzp
    endif  
  elseif @converge == 8                      ; Mixed2
    if  iterate % 2 == 0
      #z = #z - 2*fz*fzp/(2*fzp^2 - fz*fzp2)  
    else
      #z = #z - fz/fzp
    endif
  elseif @converge == 9                      ; Mixed3
    if  iterate % 2 == 0
      #z = #z - fz*fzp/(fzp^2 - fz*fzp2)  
    else
      #z = #z - fz/fzp
    endif
  elseif @converge == 10                      ; Mixed4
    if  iterate % 2 == 0
      #z = #z - @custom*fz*fzp/(@custom*fzp^2 - fz*fzp2)  
    else
      #z = #z - fz/fzp
    endif
  endif  
bailout:
  |#z - oldz| >= @bailout
default:
  title = "Cayley Julia"
  maxiter = 1000
  center = (0, 0)
  magn = 32
  method = multipass
  periodicity = 0
  heading
    caption = "Cayley Julia"
  endheading
$ifdef VER40
  heading
    text = "This is a 'convergent' fractal that uses multiple convergence \
            methods and has Julia-like regions for several convergence methods."
  endheading
$else
  heading
    caption = "This is a 'convergent' fractal"
  endheading
  heading
    caption = "that uses multiple convergence"
  endheading
  heading
    caption = "methods and has Julia-like regions"
  endheading
  heading
    caption = "for several convergence methods."
  endheading
$endif
  param version
    caption = "Formula Version"
    default = 1.0
    hint = "You should never see this parameter; it's used internally to track \
        which version of the formula was used to create your image, so that \
        if a bug is found which breaks backwards-compatibility, the formula \
        can adapt transparently."
    visible = false
  endparam
  param bailout
    caption = "Bailout value"
    default = 0.000001
  endparam
  param p1
    caption = "Parameter 1"
    default = (0.360968017578125,0.00074462890625)
  endparam
  heading
    caption = "Convergence Methods"
  endheading  
  param converge
    caption = "Convergence Method"
    default = 0
    enum = "Newton" "Householder" "Halley" "Schroder" "Ho Custom" \
           "Ha Custom" "H_S Custom" "Mixed1" "Mixed2" "Mixed3" "Mixed4"
  endparam  
  float param custom
    caption = "H_S Constant"
    default = 1.5
    visible = @converge==4 || @converge==5  || @converge==6 || @converge==10
  endparam
switch:
  type = "Cayley-mand"
  bailout = @bailout
  converge = @converge
  custom = @custom
}
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Cayley-jul-NEWTON.gsp (22.09 KB)
以上源文件中,将迭代终点到三根的距离引进颜色参数后,扫出的图片。
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JD-SG-02.JPG
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JDfrm010.JPG
我认为学习复分形,UF中的范例是最好的范例,所以我还是坚持将里面漂亮的范例,演绎完。
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柳老师能否说明一下是如何处理whitesq这个逻辑变量的?这个JD-SG系列演绎的相当棒。
29# 榕坚
我是看到此系列的分形在UF中不是一次形成的,好象都是经过两次图层的叠加而成。其它的分形几乎都是立即成象。所以我是分别造两个复分形,然后将扫出的两个轨迹叠加在一起。不知对也不对。
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