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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 2799
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附件: z3-1N集.gsp (2012-7-25 15:07, 23.55 KB) / 下载次数 5268
http://forums.netpad.net.cn/attachment.php?aid=18041&k=57135a780e7c17405d7e9da28d47a229&t=1779824244&sid=2ra32n

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 2839
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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 2820
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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 2935
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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)

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附件: z3-2z+2N集.gsp (2012-12-17 19:40, 25.31 KB) / 下载次数 5094
http://forums.netpad.net.cn/attachment.php?aid=19134&k=bc047eb9dd39bbf839d139b8afdb9ce5&t=1779824244&sid=2ra32n

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 2791
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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 2836
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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：

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http://forums.netpad.net.cn/attachment.php?aid=18079&k=5c38c28975b0dc2b42e6063297012bbd&t=1779824244&sid=2ra32n

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 1461
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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 1424
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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 1442
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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 1373
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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 1387
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作者: 柳烟 时间: 2015-2-15 17:45

又是别样风味：

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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)

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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 3133
http://forums.netpad.net.cn/attachment.php?aid=23744&k=5910767214bbb3665324cf1eb1570915&t=1779824244&sid=2ra32n

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 3043
http://forums.netpad.net.cn/attachment.php?aid=23752&k=cc0dc1a8fb21754a99ba76b82700f780&t=1779824244&sid=2ra32n

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)

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附件: M集20150119.gsp (2015-2-19 00:15, 13.78 KB) / 下载次数 3027
http://forums.netpad.net.cn/attachment.php?aid=23757&k=11ad11211f750e51ca08eddf6ad5082c&t=1779824244&sid=2ra32n

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 1272
http://forums.netpad.net.cn/attachment.php?aid=23758&k=287662aac73fd91703271573c63585e4&t=1779824244&sid=2ra32n

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 2108
http://forums.netpad.net.cn/attachment.php?aid=23759&k=9e29af94007dda49cda01fa37343404f&t=1779824244&sid=2ra32n

附件: 未命名3.gsp (2015-2-19 10:41, 14.68 KB) / 下载次数 2129
http://forums.netpad.net.cn/attachment.php?aid=23760&k=5700c3253c683d9409bca5fbafdcfa3c&t=1779824244&sid=2ra32n

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 1938
http://forums.netpad.net.cn/attachment.php?aid=23761&k=6b5aae852d542247201967338d8a386d&t=1779824244&sid=2ra32n

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 1263
http://forums.netpad.net.cn/attachment.php?aid=23762&k=33f81fa730552407ae3426caebac23e8&t=1779824244&sid=2ra32n

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)

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附件: M集（20150219同向乌龟阵）.gsp (2015-2-19 23:05, 15.94 KB) / 下载次数 2651
http://forums.netpad.net.cn/attachment.php?aid=23764&k=750e8957c95be4f01a9fa1758bfbd584&t=1779824244&sid=2ra32n

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 1370
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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 1532
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附件: M集阵列2.gsp (2015-2-20 22:52, 12.44 KB) / 下载次数 3231
http://forums.netpad.net.cn/attachment.php?aid=23767&k=a87c4b3d0ce0a87776d7b2333de8f93a&t=1779824244&sid=2ra32n

作者: 柳烟 时间: 2015-2-21 08:16

M集阵列（20140220）.gsp (16.96 KB)

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附件: M集阵列（20140220）.gsp (2015-2-21 08:16, 16.96 KB) / 下载次数 3036
http://forums.netpad.net.cn/attachment.php?aid=23769&k=ef0c8c87bf065f95c844814dbc0e86ba&t=1779824244&sid=2ra32n

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 2675
http://forums.netpad.net.cn/attachment.php?aid=23771&k=e6f3aa78bffce77cc64b69fe722abcd2&t=1779824244&sid=2ra32n

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 1308
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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 1296
http://forums.netpad.net.cn/attachment.php?aid=23773&k=4f0712d2f1ef2607bb15ee2b3ed0d5f9&t=1779824244&sid=2ra32n

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 1393
http://forums.netpad.net.cn/attachment.php?aid=23774&k=3988a4fbc89f3cb65bb210c6961fc571&t=1779824244&sid=2ra32n

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 1286
http://forums.netpad.net.cn/attachment.php?aid=23775&k=2e41733cc883da2bf9e6171818248112&t=1779824244&sid=2ra32n

图片附件: 1.gif (2015-2-22 15:38, 47.41 KB) / 下载次数 1320
http://forums.netpad.net.cn/attachment.php?aid=23776&k=129f4fec08116c23eb0c2e6dabc9e0ec&t=1779824244&sid=2ra32n

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 1308
http://forums.netpad.net.cn/attachment.php?aid=23778&k=ecebed1320ad9ab3cdbc057f808a5fc3&t=1779824244&sid=2ra32n

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 1347
http://forums.netpad.net.cn/attachment.php?aid=23779&k=ca47d614e62c099ed83561154127f45a&t=1779824244&sid=2ra32n

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 3191
http://forums.netpad.net.cn/attachment.php?aid=23780&k=b735129609bc526b5406a0b6ef25560e&t=1779824244&sid=2ra32n

图片附件: New.gif (2015-2-22 23:57, 32.68 KB) / 下载次数 1347
http://forums.netpad.net.cn/attachment.php?aid=23781&k=f08edbfdb888e04dbccce1a9b5070886&t=1779824244&sid=2ra32n

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 1452
http://forums.netpad.net.cn/attachment.php?aid=23782&k=549e0c91082e9b90b59903efca5b7a85&t=1779824244&sid=2ra32n

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 1467
http://forums.netpad.net.cn/attachment.php?aid=23786&k=098dccf743a867cf778a421ba99463fe&t=1779824244&sid=2ra32n

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 3252
http://forums.netpad.net.cn/attachment.php?aid=23787&k=43c721e734d661d926cb3e684e8a69ed&t=1779824244&sid=2ra32n

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 1457
http://forums.netpad.net.cn/attachment.php?aid=23788&k=10eaf70194b706f1476972fd9e99a546&t=1779824244&sid=2ra32n

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 3489
http://forums.netpad.net.cn/attachment.php?aid=23789&k=ee318e1dbe7fcf2ad84252bc231c36e1&t=1779824244&sid=2ra32n

图片附件: 1.gif (2015-2-24 21:27, 29.27 KB) / 下载次数 1452
http://forums.netpad.net.cn/attachment.php?aid=23790&k=077a4bdd360bb1bb06c46a637d49ae8a&t=1779824244&sid=2ra32n

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 1458
http://forums.netpad.net.cn/attachment.php?aid=23791&k=81a09df3e19a971c3a886ffb51638290&t=1779824244&sid=2ra32n

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