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标题: newton集根作色法与分形阵列（征解） [打印本页]

作者: 柳烟 时间: 2012-7-23 17:02 标题: newton集根作色法与分形阵列（征解）

胡乱整一幅用根作色法调色的牛集分形，很不满意。不知有没有一本万利的分块作色法，从FSK软件来看，好象有。

z3-1N集.gsp (23.55 KB)

图片附件: 1.jpg (2015-2-15 08:19, 13.73 KB) / 下载次数 2227
http://www.inrm3d.cn/attachment.php?aid=18035&k=f0c47ecb8869a4c159e8dde106ed94d7&t=1716027630&sid=RkKzKS

附件: z3-1N集.gsp (2012-7-25 15:07, 23.55 KB) / 下载次数 4434
http://www.inrm3d.cn/attachment.php?aid=18041&k=4bec87989dd89a0ffb20e374fbd618f8&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-7-23 20:38

图片附件: 2.jpg (2015-2-15 08:20, 16.77 KB) / 下载次数 2297
http://www.inrm3d.cn/attachment.php?aid=18038&k=ebf0da13fc33db4b380e52ff32692daa&t=1716027630&sid=RkKzKS

图片附件: 3.jpg (2015-2-15 08:20, 20.3 KB) / 下载次数 2198
http://www.inrm3d.cn/attachment.php?aid=18040&k=540d5757928b3227352887fa6b2580a2&t=1716027630&sid=RkKzKS

作者: xiaongxp 时间: 2012-7-23 21:00

2# 柳烟
着色非常鲜亮。

作者: 柳烟 时间: 2012-7-23 21:35

3# xiaongxp
问好向老师。

如何让等势圈抹去，并出现高亮效果，目前我还没有好计谋。

图片附件: 4.jpg (2015-2-15 08:21, 21.34 KB) / 下载次数 2253
http://www.inrm3d.cn/attachment.php?aid=18043&k=802d69bb6eac818449bd7d3a67301189&t=1716027630&sid=RkKzKS

作者: changxde 时间: 2012-7-24 10:21

不用et可去等势圈，
用彩带可去等势圈，FSK好像也是彩带。
UF中有没有相关着色，我没发现。

作者: xiaongxp 时间: 2012-7-24 10:31

4# 柳烟
彩色N集的等势线抹去后就没有层次感了，只能设法使其变得色彩过渡更平滑。若只凸显项链结构，用浮雕法弱化外部等势线并灰度着色为佳。

图片附件: 11.jpg (2012-7-24 10:31, 47.41 KB) / 下载次数 2316
http://www.inrm3d.cn/attachment.php?aid=18048&k=6c72d7aa6d59b537e9af76442dfda9a7&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-7-24 13:31

一并问好以上二位老友。以前不可思议的分形，通过大家的不懈努力并求索，不断获得解决。用根作色法，扫一张网上的分形，此分形原来作过，着色老是不尽人意，今用根作色，并用调色板颜色染之，自觉可以乱真了。

http://www.inrm3d.cn/viewthread. ... F7%D6%AE&page=1

z3-2z+2N集.gsp (25.31 KB)

图片附件: 5.jpg (2015-2-15 08:22, 18.82 KB) / 下载次数 2240
http://www.inrm3d.cn/attachment.php?aid=18049&k=0514b980c0e0e636e85532203a377f1c&t=1716027630&sid=RkKzKS

附件: z3-2z+2N集.gsp (2012-12-17 19:40, 25.31 KB) / 下载次数 4285
http://www.inrm3d.cn/attachment.php?aid=19134&k=8aaf9963d2a694eabc614d77b481224f&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-7-24 16:08

再扫一幅：

图片附件: 6.jpg (2015-2-15 08:23, 17.02 KB) / 下载次数 2245
http://www.inrm3d.cn/attachment.php?aid=18050&k=18cf4ec7bced75d78e93e81b4a63f3d7&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-7-24 16:49

来自网上图片，函数式f(z)=z^5+2*z^4+3*z^3-4*z^2-5*z-6，如何求出这个方程的近似根呢？

图片附件: newtonbasin1.jpg (2012-7-25 07:22, 29.33 KB) / 下载次数 2273
http://www.inrm3d.cn/attachment.php?aid=18052&k=0fa9b18e2aa93c026f68405dea7569a5&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-7-24 23:16

根作色法先要求出方程的根，这要用到常老师的三四次方程求根工具。见该论坛。勉强弄一幅：

图片附件: 7.jpg (2015-2-15 08:24, 15.86 KB) / 下载次数 2283
http://www.inrm3d.cn/attachment.php?aid=18055&k=3b35e7856186d3fa30af0d40a9f10dae&t=1716027630&sid=RkKzKS

图片附件: 8.jpg (2015-2-15 08:24, 15.71 KB) / 下载次数 2246
http://www.inrm3d.cn/attachment.php?aid=18079&k=dc49b35926a5eda91cf43b9e6a885ddf&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-7-25 14:23

将根作色法用于牛M集，还行。

忍不住，再扫一幅：

以上各分形着色算法，均采用#1楼源文件给出的算法进行。
这是(z^2-1)(z^2-c^2)的牛M集

图片附件: 9.jpg (2015-2-15 08:25, 12.04 KB) / 下载次数 1160
http://www.inrm3d.cn/attachment.php?aid=18057&k=57c3b4ee15f5dcf46f97b09a9fb3d1fc&t=1716027630&sid=RkKzKS

图片附件: a.jpg (2015-2-15 08:25, 20.43 KB) / 下载次数 1159
http://www.inrm3d.cn/attachment.php?aid=18063&k=7e7f8746f826c06c621259490526b026&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-7-26 12:10

柳烟作品：z^6-3iz^3-2的牛集：

图片附件: b.jpg (2015-2-15 08:25, 18.31 KB) / 下载次数 1136
http://www.inrm3d.cn/attachment.php?aid=18062&k=b744b2448b91ec60678997cf292b533c&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-7-26 18:05

用根作色法演绎UF中的Ikenaga Roots-Mandel：

图片附件: c.jpg (2015-2-15 08:26, 14.63 KB) / 下载次数 1139
http://www.inrm3d.cn/attachment.php?aid=18071&k=170de2592fa7f451ad2009f38e886884&t=1716027630&sid=RkKzKS

图片附件: d.jpg (2015-2-15 08:26, 14.22 KB) / 下载次数 1179
http://www.inrm3d.cn/attachment.php?aid=18074&k=bd45b3696fbc3346c9facbfadcab92ec&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2012-8-1 02:43

一边看伦登奥运举重，一边关注扫图。
将根作色法与光滑牛集作色法结合起来，造一幅：

图片附件: e.jpg (2015-2-15 08:27, 24.73 KB) / 下载次数 1110
http://www.inrm3d.cn/attachment.php?aid=18174&k=867b473390544d4124b6b766cfbfc48a&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-15 00:00

用HSV作色：

图片附件: f.jpg (2015-2-15 08:28, 16.4 KB) / 下载次数 1109
http://www.inrm3d.cn/attachment.php?aid=23740&k=92e461d92a6458ac5b0a04efcf2b8df9&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-15 17:45

又是别样风味：

图片附件: g.jpg (2015-2-15 18:46, 22.59 KB) / 下载次数 1092
http://www.inrm3d.cn/attachment.php?aid=23741&k=5a849ce7cc87b5c93fc092b3cd1f2249&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-16 09:01

f(z)=z^5+2*z^4+3*z^3-4*z^2-5*z-6的N集，根作色。此多项式的五个根用magle软件求出。

f(z)=z5+2z4+3z3-4z2-5z-6.gsp (32.73 KB)

图片附件: g.jpg (2015-2-16 13:39, 20.8 KB) / 下载次数 1182
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附件: f(z)=z5+2z4+3z3-4z2-5z-6.gsp (2015-2-16 09:32, 32.73 KB) / 下载次数 2696
http://www.inrm3d.cn/attachment.php?aid=23744&k=521dbc2374e237c8cf27f9007dd2f267&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-17 19:31

(z2-1)(z2-c2)的N集.gsp (25.4 KB)

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附件: (z2-1)(z2-c2)的N集.gsp (2015-2-17 19:48, 25.4 KB) / 下载次数 2579
http://www.inrm3d.cn/attachment.php?aid=23752&k=7e96d9f47b0156fa29fe40abaea932dc&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-19 00:06

将M集加点对称平移变换：

M集20150119.gsp (13.78 KB)

图片附件: 1.gif (2015-2-22 15:20, 62.55 KB) / 下载次数 1173
http://www.inrm3d.cn/attachment.php?aid=23756&k=af32a847ac7524501b551c3a2ff0bed9&t=1716027630&sid=RkKzKS

附件: M集20150119.gsp (2015-2-19 00:15, 13.78 KB) / 下载次数 2583
http://www.inrm3d.cn/attachment.php?aid=23757&k=6e40bf2c2f18605341a33aeed6de76a9&t=1716027630&sid=RkKzKS

作者: xiaongxp 时间: 2015-2-19 00:20

柳老师新年好！
柳老师好用功哦，大年年关扫图，令人感动。

作者: 柳烟 时间: 2015-2-19 01:04

20# xiaongxp
向老师新年快乐！晚上无事，又无睡意，对打麻将等又没兴趣，看看电视，玩玩电脑，混时间呗。

作者: 柳烟 时间: 2015-2-19 01:30

Mandelbrot {
;
; Generic Mandelbrot set.
;
init:
  z = @start
  c= #pixel
  x=real(c)
  y=imag(c)
  int k=0
  while (k<@TH)
  x=abs(x)-2.5
  y=abs(y)-2
  k = k+1
  endwhile
  x=abs(x)-2
  y=abs(y)-1
  c=x+flip(y)
loop:
  z = z^@power + c
bailout:
  |z| <= @bailout
default:
  title = "Mandelbrot"
  center = (-0.5, 0)
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  param start
caption = "Starting point"
default = (0,0)
hint = "The starting point parameter can be used to distort the Mandelbrot \
         set. Use (0, 0) for the standard Mandelbrot set."
  endparam
  param power
caption = "Power"
default = (2,0)

  endparam
  param TH
caption = "th"
default = 5

  endparam
  float param bailout
caption = "Bailout value"
default = 4.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
         iterating. Larger values give smoother outlines; values around 4 \
         give more interesting shapes around the set. Values less than 4 \
         will distort the fractal."
  endparam
}

图片附件: 2.gif (2015-2-22 15:22, 34.04 KB) / 下载次数 1019
http://www.inrm3d.cn/attachment.php?aid=23758&k=9e65ddab1d087eacdce920229fcdcc6d&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-19 01:32

如何将一个乌龟通过变换，变成指针均往左或右的乌龟阵势？有了点想法，但不知能否实现。

作者: zhongba 时间: 2015-2-19 10:00

23# 柳烟

附件: 未命名2.gsp (2015-2-19 10:00, 3.75 KB) / 下载次数 1760
http://www.inrm3d.cn/attachment.php?aid=23759&k=72e727a088ef2ee673bcc230b698e0d5&t=1716027630&sid=RkKzKS

附件: 未命名3.gsp (2015-2-19 10:41, 14.68 KB) / 下载次数 1761
http://www.inrm3d.cn/attachment.php?aid=23760&k=c9cd918b814927973e856f6e7577426b&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-19 16:25

24# zhongba
谢谢精妙文件，设计十分巧妙。

作者: zhongba 时间: 2015-2-19 21:46

24# zhongba
精简了一下

附件: [20日凌晨再精简] M集阵列.gsp (2015-2-20 01:08, 12.35 KB) / 下载次数 1600
http://www.inrm3d.cn/attachment.php?aid=23761&k=54417260f1b5b67910cec9396251d84a&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-19 21:51

受24楼文件启发：
Mandelbrot同向阵列 {

init:
  z = @start
  c= #pixel
  x=real(c)
  y=imag(c)
  x=x+13-trunc(x+13)
  y=y+13-trunc(y+13)
  c=4*(x+flip(y)+(-0.7,-0.5))
loop:
z = z^@power + c
bailout:
  |z| <= @bailout
default:
  title = "Mandelbrot同向阵列"
  center = (0, 0)
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  param start
caption = "Starting point"
default = (0,0)
hint = "The starting point parameter can be used to distort the Mandelbrot \
         set. Use (0, 0) for the standard Mandelbrot set."
  endparam
  param power
caption = "Power"
default = (2,0)

  endparam
  float param bailout
caption = "Bailout value"
default = 4.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
         iterating. Larger values give smoother outlines; values around 4 \
         give more interesting shapes around the set. Values less than 4 \
         will distort the fractal."
  endparam

}

图片附件: Fractal2.png (2015-2-19 21:51, 30.71 KB) / 下载次数 999
http://www.inrm3d.cn/attachment.php?aid=23762&k=a8208d7380f8e18d714cfdc11c00a45a&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-19 22:50

将就原M集，加点变换：

M集（20150219同向乌龟阵）.gsp (15.94 KB)

图片附件: 3.gif (2015-2-22 15:24, 38.29 KB) / 下载次数 1002
http://www.inrm3d.cn/attachment.php?aid=23763&k=693901a853b91a0538e21c603da212ef&t=1716027630&sid=RkKzKS

附件: M集（20150219同向乌龟阵）.gsp (2015-2-19 23:05, 15.94 KB) / 下载次数 2248
http://www.inrm3d.cn/attachment.php?aid=23764&k=82360dace4ee4e9430252d953e5d72db&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-19 23:24

M集反向乌龟阵UF法：
Mandelbrot阵列 {
;
; Generic Mandelbrot set.
;
init:
  z = @start
  c= #pixel
  x=tan(cos(real(c)))-1
  y=tan(cos(imag(c)))
  c=x+flip(y)
loop:
  z = z^@power + c
bailout:
  |z| <= @bailout
default:
  title = "Mandelbrot反向乌龟阵"
  center = (-0.5, 0)
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  param start
caption = "Starting point"
default = (0,0)
hint = "The starting point parameter can be used to distort the Mandelbrot \
         set. Use (0, 0) for the standard Mandelbrot set."
  endparam
  param power
caption = "Power"
default = (2,0)
hint = "This parameter sets the exponent for the Mandelbrot formula. \
         Increasing the real part to 3, 4, and so on, will add discs to \
         the Mandelbrot figure. Non-integer real values and non-zero \
         imaginary values will create distorted Mandelbrot sets. Use (2, 0) \
         for the standard Mandelbrot set."
  endparam
  float param bailout
caption = "Bailout value"
default = 4.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
         iterating. Larger values give smoother outlines; values around 4 \
         give more interesting shapes around the set. Values less than 4 \
         will distort the fractal."
  endparam
switch:
  type = "Julia"
  seed = #pixel
  power = power
  bailout = bailout
}

图片附件: Fractal4.png (2015-2-19 23:24, 51.01 KB) / 下载次数 1092
http://www.inrm3d.cn/attachment.php?aid=23765&k=caff0bb6cbc2a7ba49fb3cba271aa433&t=1716027630&sid=RkKzKS

作者: xiaongxp 时间: 2015-2-20 22:52

M集阵列2.gsp (12.44 KB)

图片附件: M集阵列2.jpg (2015-2-20 22:52, 37.63 KB) / 下载次数 1237
http://www.inrm3d.cn/attachment.php?aid=23766&k=3a3e8c9e1bf020a28d7ab1dfa0d2d992&t=1716027630&sid=RkKzKS

附件: M集阵列2.gsp (2015-2-20 22:52, 12.44 KB) / 下载次数 2737
http://www.inrm3d.cn/attachment.php?aid=23767&k=9f55acc9ea42a929e84110591b50a024&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-21 08:16

M集阵列（20140220）.gsp (16.96 KB)

图片附件: 4.gif (2015-2-22 15:26, 40.49 KB) / 下载次数 1031
http://www.inrm3d.cn/attachment.php?aid=23768&k=7f4de7d0d4dfca4ec39b561f411256f4&t=1716027630&sid=RkKzKS

附件: M集阵列（20140220）.gsp (2015-2-21 08:16, 16.96 KB) / 下载次数 2611
http://www.inrm3d.cn/attachment.php?aid=23769&k=e078d3bfe5ea6dbc13c3a7c64d5b277a&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-21 11:27

M集行阵（20150221(1)）.gsp (18.42 KB)

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附件: M集行阵（20150221(1)）.gsp (2015-2-21 11:28, 18.42 KB) / 下载次数 2269
http://www.inrm3d.cn/attachment.php?aid=23771&k=dae413628661d399037f6c7b297433aa&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-21 13:38

图片附件: 6.gif (2015-2-22 15:29, 35.12 KB) / 下载次数 1032
http://www.inrm3d.cn/attachment.php?aid=23772&k=6c0acd6ba706e5672b5b457939162f01&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-21 19:47

Mandelbrot阵列20150221(1号) {

init:
  z = @start
  c= 4*#pixel
  x=real(c)
  y=imag(c)
  int  k=0
  while (k<@hp)
  x=abs(x)-6
  y=abs(y)-6
  k=k+1
  endwhile
  x=abs(x)-3
  y=abs(y)-3
  m=sqrt(3)*x-y
  n=sqrt(3)*x+y
  IF n>0&&y>0
  s=2*pi/3

  elseif m>0&&y<0
  s=-2*pi/3
  endif
  c=x+flip(y)
  c=c*exp(1i*s)+1
loop:
  z = z^@power + c
bailout:
  |z| <= @bailout
default:
  title = "Mandelbrot乌龟阵20150221(1号)"
  center = (0, 0)
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  param start
caption = "Starting point"
default = (0,0)
hint = "The starting point parameter can be used to distort the Mandelbrot \
         set. Use (0, 0) for the standard Mandelbrot set."
  endparam
  param power
caption = "Power"
default = (2,0)

  endparam
param hp
caption = "hp"
default = 1

  endparam
  float param bailout
caption = "Bailout value"
default = 4.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
         iterating. Larger values give smoother outlines; values around 4 \
         give more interesting shapes around the set. Values less than 4 \
         will distort the fractal."
  endparam

}

图片附件: 7.gif (2015-2-22 15:30, 32.68 KB) / 下载次数 1031
http://www.inrm3d.cn/attachment.php?aid=23773&k=c21d245c4ac8c7fc170af9405d29fe63&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-21 20:09

Mandelbrot阵列20150221(2号) {

init:
  z = @start
  c= 7*#pixel
  x=real(c)
  y=imag(c)
  int  k=0
  while (k<@hp)
  x=abs(x)-6
  y=abs(y)-6
  k=k+1
  endwhile
  x=abs(x)-3
  y=abs(y)-3
  m=x-y
  n=x+y
  IF m<0&&n<0
  s=0
elseif m<0&&n>0
  s=pi/2
elseif m>0&&n>0
  s=-pi
elseif m>0&&n<0
  s=3*pi/2
  endif
  c=x+flip(y)
  c=c*exp(1i*s)+1
loop:
  z = z^@power + c
bailout:
  |z| <= @bailout
default:
  title = "Mandelbrot乌龟阵20150221(2号)"
  center = (0, 0)
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  param start
caption = "Starting point"
default = (0,0)
hint = "The starting point parameter can be used to distort the Mandelbrot \
         set. Use (0, 0) for the standard Mandelbrot set."
  endparam
  param power
caption = "Power"
default = (2,0)

  endparam
param hp
caption = "hp"
default = 1

  endparam
  float param bailout
caption = "Bailout value"
default = 4.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
         iterating. Larger values give smoother outlines; values around 4 \
         give more interesting shapes around the set. Values less than 4 \
         will distort the fractal."
  endparam
}

图片附件: Fractal4.png (2015-2-21 20:09, 65.17 KB) / 下载次数 1133
http://www.inrm3d.cn/attachment.php?aid=23774&k=a5368177603f987a300fe9c1acf0a0cb&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-21 23:36

造阵列，受启发，终于完成了五角星科赫雪花的UF代码：
五角星科赫雪花20150221 {
init:
z = pixel
s=0.5
arg=atan2(z)
if abs(arg+pi/10)>4*pi/5
z=z*exp(1i*4*pi/5)
endif
loop:
arg=atan2(z)
x = real(z)
y = imag(z)
L13=-y+0.30902
L35=1.11803*x+1.53884*y+0.587785
L25=1.80902*x+0.587785*y-0.587785
L24=1.80902*x-0.587785*y+0.587785
L14=1.11803*x-1.53884*y-0.587785
L1=0.32492*x+y
L2=1.37638*x-y
m1=x-(1+s)*0.95106
n1=y-(1+s)*0.30902
m2=x-(1+s)*0.58779
n2=y+(1+s)*0.80902
n3=x+(1+s)*0.58779
if  abs(arg-pi/10) <pi/5
v=m1+flip(n1)
b=-pi/5
elseif abs(arg-13*pi/20) <7*pi/20
v=x+flip(y-(1+s))
b=-3*pi/5
elseif abs(arg+3*pi/10) <pi/5
v=m2+flip(n2)
b=pi/5
elseif abs(arg+pi/4)<3*pi/4
v=n3+flip(n2)
b=3*pi/5
endif
z=1/s*v*exp(1i*b)
bailout:
(L13<=0&&L24>=0&&L25>=0)||(L13<=0&&L24<0)||(L14>=0&&L13>0&&L25>=0&&L35>=0)||(L14>=0&&L35<0)||(L13>0&&L35<0&&L24<0&&L14<0)
default:
  title = "五角星科赫雪花20150221"
  helpfile = "sam-help/various.htm"
  helptopic = "sierp2"
  center = (0,0)

}

可惜的是，原始陷阱搞掉了，在UF中不知如何用代码实现。

图片附件: Fractal5.png (2015-2-21 23:37, 46.54 KB) / 下载次数 1030
http://www.inrm3d.cn/attachment.php?aid=23775&k=317639d14a4b861b2aecebf550145f4e&t=1716027630&sid=RkKzKS

图片附件: 1.gif (2015-2-22 15:38, 47.41 KB) / 下载次数 1059
http://www.inrm3d.cn/attachment.php?aid=23776&k=8b4da7e8f4540291640a45d8f42c3cc7&t=1716027630&sid=RkKzKS

作者: zhongba 时间: 2015-2-22 00:21

36# 柳烟
五角星科赫雪花中的相邻两级迭代五角星的半径比约为1-0.618

作者: 柳烟 时间: 2015-2-22 11:46

图片附件: 8.gif (2015-2-22 15:31, 32.14 KB) / 下载次数 1052
http://www.inrm3d.cn/attachment.php?aid=23778&k=921889c47a6e444f8bdd7df2ac9a4d6b&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-22 23:35

MJ阵列20150222 {

init:
  z1 = @start
  c1= #pixel
  x=real(c1)
  c2=6*(c1+(23,23)-trunc(c1+(23,23)))-3
  x=real(c2)
if x>0
  z=z1
  c=1.2*(c2+(-2,-3))
  else
  z=1.2*(c2+(1.5,-3))
  c=@JJ
  endif
loop:
  z = z^@power + c
bailout:
  |z| <= @bailout
default:
  title = "MJ集阵列20150222"
  center = (0, 0)
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  param start
caption = "Starting point"
default = (0,0)

  endparam
param JJ
caption = "J集定位"
default = (0.356180,0.07463)

  endparam
  param power
caption = "Power"
default = (2,0)

  endparam
param hp
caption = "hp"
default = 1

  endparam
  float param bailout
caption = "Bailout value"
default = 4.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
         iterating. Larger values give smoother outlines; values around 4 \
         give more interesting shapes around the set. Values less than 4 \
         will distort the fractal."
  endparam

}
我想将行距压缩一下，结果搞了许久，没成功。用了向老师前面文件同向乌龟中的函数trunc.

图片附件: Fractal1.png (2015-2-22 23:35, 19.58 KB) / 下载次数 1077
http://www.inrm3d.cn/attachment.php?aid=23779&k=5ac50fb152148dcb82a7f705b955ad1d&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-22 23:45

MJ集平移阵列20150223.gsp (16.04 KB)

如何在GSP中将行距减少。当我减少行距时，MJ集沿纵轴方向压扁了，不好看。

附件: MJ集平移阵列20150223.gsp (2015-2-22 23:45, 16.04 KB) / 下载次数 2732
http://www.inrm3d.cn/attachment.php?aid=23780&k=b044759219b542195b6daa0b3a257495&t=1716027630&sid=RkKzKS

图片附件: New.gif (2015-2-22 23:57, 32.68 KB) / 下载次数 1077
http://www.inrm3d.cn/attachment.php?aid=23781&k=67f9be98a60c9673a6603ce200ad516c&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-23 00:03

图片附件: 3.gif (2015-2-24 21:29, 34.46 KB) / 下载次数 1155
http://www.inrm3d.cn/attachment.php?aid=23782&k=f446fda7b9fde409b679011e2dc25207&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-23 17:47

M集（20150223四乌龟阵列1号）.gsp (17.58 KB)

图片附件: 2.gif (2015-2-24 21:28, 27.05 KB) / 下载次数 1163
http://www.inrm3d.cn/attachment.php?aid=23786&k=e6c9e186c17ba0417acc5fc2c6d18609&t=1716027630&sid=RkKzKS

附件: M集（20150223四乌龟阵列1号）.gsp (2015-2-23 17:52, 17.58 KB) / 下载次数 2757
http://www.inrm3d.cn/attachment.php?aid=23787&k=505a8156d7efed60b0c4a1e5b2d8a37c&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-23 18:57

Mandelbrot 20150223四乌龟阵1号{
  z = @start
  c=#pixel
c=3*(1.5*c+(12,12)-trunc(1.5*c+(12,12)))+(-1.5,-1.5)
x=real(c)
y=imag(c)
m=x-y
n=x+y
if m<0&&n<0
  s=pi/2
elseif m<0&&n>0
s=pi
elseif m>0&&n>0
s=-pi/2
endif
c=3*c*exp(1i*s)+(-0.5,1.8)
loop:
  z = z^@power + c
bailout:
  |z| <= @bailout
default:
  title = "Mandelbrot四乌龟阵列20150223一号"
  center = (0, 0)
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  param start
caption = "Starting point"
default = (0,0)
hint = "The starting point parameter can be used to distort the Mandelbrot \
         set. Use (0, 0) for the standard Mandelbrot set."
  endparam
  param power
caption = "Power"
default = (2,0)
hint = "This parameter sets the exponent for the Mandelbrot formula. \
         Increasing the real part to 3, 4, and so on, will add discs to \
         the Mandelbrot figure. Non-integer real values and non-zero \
         imaginary values will create distorted Mandelbrot sets. Use (2, 0) \
         for the standard Mandelbrot set."
  endparam
  float param bailout
caption = "Bailout value"
default = 1000000.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
         iterating. Larger values give smoother outlines; values around 4 \
         give more interesting shapes around the set. Values less than 4 \
         will distort the fractal."
  endparam

}

图片附件: Fractal2.png (2015-2-23 19:01, 30.61 KB) / 下载次数 1160
http://www.inrm3d.cn/attachment.php?aid=23788&k=a30657eebd808d3125265aea040bf236&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-23 23:03

M集对称变换4乌龟（20150223四乌龟阵列2号）.gsp (18.61 KB)

附件: M集对称变换4乌龟（20150223四乌龟阵列2号）.gsp (2015-2-23 23:03, 18.61 KB) / 下载次数 3008
http://www.inrm3d.cn/attachment.php?aid=23789&k=34dd1522331435acf7972a06a8afc3f8&t=1716027630&sid=RkKzKS

图片附件: 1.gif (2015-2-24 21:27, 29.27 KB) / 下载次数 1157
http://www.inrm3d.cn/attachment.php?aid=23790&k=a206e8e4874a934e874e83453045a029&t=1716027630&sid=RkKzKS

作者: 柳烟 时间: 2015-2-23 23:21

Mandelbrot 20150223四乌龟阵2号{
  z = @start
  c=4.5*#pixel
  K=0
while (k<@hp)
  c=abs(c)-(3,3)
  k=k+1
  endwhile
c=abs(c)-(1.5,1.5)
m=real(c)-imag(c)
n= real(c)+imag(c)
if m<0&&n<0
  s=pi/2
elseif m<0&&n>0
s=pi
elseif m>0&&n>0
s=-pi/2
endif
c=3*c*exp(1i*s)+(-0.5,1.8)
loop:
  z = z^@power + c
bailout:
  |z| <= @bailout
default:
  title = "Mandelbrot四乌龟阵列20150223二号"
  center = (0, 0)
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\mandelbrot.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  param start
caption = "Starting point"
default = (0,0)
hint = "The starting point parameter can be used to distort the Mandelbrot \
         set. Use (0, 0) for the standard Mandelbrot set."
  endparam
param hp
caption = "hp"
default = 1
  endparam
  param power
caption = "Power"
default = (2,0)
hint = "This parameter sets the exponent for the Mandelbrot formula. \
         Increasing the real part to 3, 4, and so on, will add discs to \
         the Mandelbrot figure. Non-integer real values and non-zero \
         imaginary values will create distorted Mandelbrot sets. Use (2, 0) \
         for the standard Mandelbrot set."
  endparam
  float param bailout
caption = "Bailout value"
default = 1000000.0
min = 1.0
$IFDEF VER40
exponential = true
$ENDIF
hint = "This parameter defines how soon an orbit bails out while \
         iterating. Larger values give smoother outlines; values around 4 \
         give more interesting shapes around the set. Values less than 4 \
         will distort the fractal."
  endparam

}

图片附件: Fractal2.png (2015-2-23 23:25, 46.41 KB) / 下载次数 1161
http://www.inrm3d.cn/attachment.php?aid=23791&k=8f1e95d1dad85a07355f5ed282042328&t=1716027630&sid=RkKzKS

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