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标题: UF与GSP合研复分形 [打印本页]

作者: 柳烟 时间: 2016-8-18 22:08 标题: UF与GSP合研复分形

这是此坛大家讨论过的复分形，以前看大家的讨论帖子，似懂非懂。现在再研究之，由迷糊到清晰，有些收获，今放到此，望起到抛砖引玉的作用。
The Mandelbrot set for (1 - z2)/(z - z2cos(z)) + cM20160817{
;
; Generic Julia set.
;
init:

  c =3*#pixel
  z=1.5445654699195
loop:
  z0=z
  z =(1-z^2)/(z-z^2*cos(z)) +c
  z =(1-z^2)/(z-z^2*cos(z)) +c
bailout:
  |z-z0| >= @bailout&&|z|<=120
default:
  title = "The Mandelbrot set for (1 - z2)/(z - z2cos(z)) + cM"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\julia.html"
$IFDEF VER50
  rating = recommended
$ENDIF
param bailout
caption = "Bailout value"
default = 0.00001
min = 0.0

$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 = "Mandelbrot"
  power = power
  bailout = bailout
}

作者: 柳烟 时间: 2016-8-18 22:17

（1-z^2)除以（z-z^2cosz)的M集20160818.gsp (20.98 KB)
无标题1.jpg

图片附件: Zwv.jpg (2016-8-20 08:04, 28.66 KB) / 下载次数 1870
http://inrm3d.cn/attachment.php?aid=24960&k=9c1721b90c7b63b06883a7d4d0f8fcaf&t=1732400877&sid=QqS2X2

附件: （1-z^2)除以（z-z^2cosz)的M集20160818.gsp (2016-8-18 22:33, 20.98 KB) / 下载次数 3630
http://inrm3d.cn/attachment.php?aid=24961&k=46d7fab9e8e746e7b96e3fc09d29c89e&t=1732400877&sid=QqS2X2

图片附件: 无标题1.jpg (2016-8-20 08:04, 16.02 KB) / 下载次数 1825
http://inrm3d.cn/attachment.php?aid=24962&k=08bf60ab298dbb5ce02b26317fc012be&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-18 22:42

定位：－0.478228114006905+0.049932680209967 i
放大倍数：84047.09100

最左边那块里的小M集，埋得相当深，UF中能发现，在GSP中，按UF来放大结果成马赛克。下面是两软件都能正常扫出的定位与放大倍数
定位：-3.0530657790553349838+0.000994311155878614254425 i
放大倍数：3.3817677E10

图片附件: 14.jpg (2016-8-20 08:02, 17.38 KB) / 下载次数 1860
http://inrm3d.cn/attachment.php?aid=24963&k=f1af89a3a57584333a6326a311ad9d39&t=1732400877&sid=QqS2X2

图片附件: 45.jpg (2016-8-20 08:02, 26.32 KB) / 下载次数 1852
http://inrm3d.cn/attachment.php?aid=24964&k=2571c92d648615f823bf95277021940f&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-19 13:38

M201608191337 {
;
; Generic Julia set.
;
init:

  c =3*#pixel
  z=0
loop:
  z0=z
  z =z^2 +c
  z =(1-z^2)/(z-z^2*cos(z)) +c

bailout:
  |z-z0| >= @bailout&&|z|<=120
default:
  title = "M201608191337"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\julia.html"
$IFDEF VER50
  rating = recommended
$ENDIF
param bailout
caption = "Bailout value"
default = 0.00001
min = 0.0

$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 = "Mandelbrot"
  power = power
  bailout = bailout
}

在如是混沌的大M中找小M，在GSP中如大海捞针，在UF中找之不易，但比画板快。

图片附件: Fractal3.jpg (2016-8-20 08:00, 50.13 KB) / 下载次数 2058
http://inrm3d.cn/attachment.php?aid=24967&k=422b491cb3b586dd4400b1725675e940&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-19 15:06

定位：-0.130922182998915-3.200985271711e-6 i
放大倍数：19790.037

201608191401M集.gsp (16.81 KB)
定位：0.419639209432235+ 0.14004931643909 i
放大倍数：19790.037

图片附件: 12.jpg (2016-8-20 07:59, 44.84 KB) / 下载次数 1880
http://inrm3d.cn/attachment.php?aid=24965&k=1a4f37601df88de7c88497b45aec871c&t=1732400877&sid=QqS2X2

附件: 201608191401M集.gsp (2016-8-19 15:06, 16.81 KB) / 下载次数 3650
http://inrm3d.cn/attachment.php?aid=24966&k=f5a2318050b0c90af9769232ff5be32d&t=1732400877&sid=QqS2X2

图片附件: 13.jpg (2016-8-20 07:59, 39.94 KB) / 下载次数 1866
http://inrm3d.cn/attachment.php?aid=24968&k=21aa8667021d0867d42799c48007e128&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-19 16:45

M201608191644 {
;
; Generic Julia set.
;
init:

  c =3*#pixel
  z=1.5445654699195
loop:
  z0=z
  z =(1-z^2)/(z-z^2*cos(z)) +c
  z =z^2 +c
bailout:
  |z-z0| >= @bailout&&|z|<=13
default:
  title = "M201608191644"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\julia.html"
$IFDEF VER50
  rating = recommended
$ENDIF
param bailout
caption = "Bailout value"
default = 0.00001
min = 0.0

$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 = "Mandelbrot"
  power = power
  bailout = bailout
}

作者: 柳烟 时间: 2016-8-19 18:56

定位：0.44136818689914+0.136526563444065 i
放大倍数：9558.8151

图片附件: 3.jpg (2016-8-20 07:57, 21.63 KB) / 下载次数 1867
http://inrm3d.cn/attachment.php?aid=24969&k=7c0c15c604a1483df5fdddaec38a4574&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-19 19:05

复合函数的零点确定很有规律，都能通过放大大M后找到小M。#6楼，函数f(z)=(1-z^2)/(z-z^2cos(z))的导数f'(z)的任一零点均可。另函数f(z)+c=0的零点也可以。
用maple算出f'(z)的一个复根为：

将#6代码中的z的初始值由z=1.5445654699195换成z=(-1.108647299,-.8001950999),仍能扫出标致的小M，十分漂亮。

图片附件: 复要.jpg (2016-8-19 23:16, 30.83 KB) / 下载次数 1870
http://inrm3d.cn/attachment.php?aid=24970&k=729934de2bb268a295b8b51c1698c559&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-20 00:27

代码中的|z|<=13中的13改为8

M20160819200042.gsp (16.9 KB)

图片附件: 34.jpg (2016-8-20 07:56, 24.81 KB) / 下载次数 1887
http://inrm3d.cn/attachment.php?aid=24972&k=b72e6d4be64292cef080e33f90cf319c&t=1732400877&sid=QqS2X2

图片附件: 11.jpg (2016-8-20 07:56, 12.64 KB) / 下载次数 1842
http://inrm3d.cn/attachment.php?aid=24973&k=876abaac35a414a2dcfe093c491d99dc&t=1732400877&sid=QqS2X2

附件: M20160819200042.gsp (2016-8-20 00:49, 16.9 KB) / 下载次数 3757
http://inrm3d.cn/attachment.php?aid=24974&k=70094d945825c40677c1437bd47b9d64&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-20 02:22

图片附件: 98.jpg (2016-8-20 07:53, 39.69 KB) / 下载次数 1859
http://inrm3d.cn/attachment.php?aid=24975&k=75a16fa905f7bb468d36399474d83f47&t=1732400877&sid=QqS2X2

图片附件: 97.jpg (2016-8-20 07:53, 32.01 KB) / 下载次数 1850
http://inrm3d.cn/attachment.php?aid=24976&k=5cb2b1e9ec54b47d73637b78535e0994&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-20 07:57

怪，GSP中图没有8个小圆饼环绕小M，而UF中有，不明所以了。

图片附件: 怪1.jpg (2016-8-20 08:06, 27.97 KB) / 下载次数 1421
http://inrm3d.cn/attachment.php?aid=24977&k=ce98755153cb33cd09b004c661de4506&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-20 08:30

找到原因了，原来是阀值的问题。

图片附件: 11.jpg (2016-8-20 18:19, 36.08 KB) / 下载次数 1428
http://inrm3d.cn/attachment.php?aid=24978&k=25b345954ad7dbc3e3f82329c16779a8&t=1732400877&sid=QqS2X2

图片附件: 7.jpg (2016-8-20 18:19, 51.9 KB) / 下载次数 1587
http://inrm3d.cn/attachment.php?aid=24979&k=65ae6a821478266eb6d73fda3af1a1cf&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-20 16:11

图片附件: 12.jpg (2016-8-20 18:20, 28.63 KB) / 下载次数 1452
http://inrm3d.cn/attachment.php?aid=24980&k=bc98ccdaaae22385ab9e620ccf46898b&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-20 16:54

M201608201639{
;
; Generic Julia set.
;
init:

  c =3*#pixel
  z=-1.663892103
loop:
  z0=z
  z =(1-z^2)/(z-z^2*sin(z)) +c
  z =(1-z^2)/(z-z^2*sin(z)) +c
bailout:
  |z|<=23&&|z-z0|>=0.00001
default:
  title = " M201608201639"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\julia.html"
$IFDEF VER50
  rating = recommended
$ENDIF
param bailout
caption = "Bailout value"
default = 0.00001
min = 0.0

$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 = "Mandelbrot"
  power = power
  bailout = bailout
}

作者: 柳烟 时间: 2016-8-20 20:00

图片附件: 132.jpg (2016-8-20 20:00, 41.95 KB) / 下载次数 1400
http://inrm3d.cn/attachment.php?aid=24981&k=bba72c46eba5047445bda8a9c6a330d5&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-20 20:17

#14楼GSP扫图一付。
调色很有趣的，胡乱调，觉得此张图感觉良好。

定位：0.90295242816667952+0 i
放大：16710923 迭代200

图片附件: 131.jpg (2016-8-28 09:22, 34.16 KB) / 下载次数 1398
http://inrm3d.cn/attachment.php?aid=24982&k=77ad90ec72c1130fb87997a5f89fddf0&t=1732400877&sid=QqS2X2

图片附件: 111.jpg (2016-8-28 09:22, 34.53 KB) / 下载次数 1368
http://inrm3d.cn/attachment.php?aid=24983&k=57051ccf765cf703401844a54b9b8112&t=1732400877&sid=QqS2X2

作者: xiaongxp 时间: 2016-8-20 21:26

16# 柳烟
这个结构美呀！

作者: 柳烟 时间: 2016-8-20 23:08

15# 柳烟
用GSP多算几个零点，先用maple求出函数的一阶导数，再在GSP中作出该函数，找出x轴交点，再用高精坐标工具找出函数的零点。

函数零值点.gsp (120.35 KB)

附件: 函数零值点.gsp (2016-8-20 23:08, 120.35 KB) / 下载次数 2931
http://inrm3d.cn/attachment.php?aid=24984&k=45c64fe4f0f33ac05566475e71cc469d&t=1732400877&sid=QqS2X2

作者: swgydt 时间: 2016-8-21 16:13

有深度，学习了。UF里找数据，画板里面来实现。其乐无穷。

作者: swgydt 时间: 2016-8-21 16:24

这里面的链接已经失效，柳老师，能否再上传一次。谢谢

图片附件: Snap2.jpg (2016-8-21 16:27, 33 KB) / 下载次数 1238
http://inrm3d.cn/attachment.php?aid=24985&k=4f1085e16697d426f52d3479acd67250&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-21 20:03

20# swgydt

Chaosbrot (Julia)的制作视频.gsp (33.59 KB)
这个分形与z^2+c的J集造法一致。我新造了视频文件，地址：
视频文件地址

以下是几年前整的旧视频：

附件: Chaosbrot (Julia)的制作视频.gsp (2016-8-21 20:03, 33.59 KB) / 下载次数 3054
http://inrm3d.cn/attachment.php?aid=24986&k=180e6e7772cb6eaf2ba61ad5c6c88178&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-21 20:17

这是新视频中用的工具，有的是我整的工具，有的是本坛老师整的。

复分形TOOLS2016更新.rar (121.33 KB)

附件: 复分形TOOLS2016更新.rar (2016-8-21 20:17, 121.33 KB) / 下载次数 2657
http://inrm3d.cn/attachment.php?aid=24987&k=00eaf496cdf56815fd1d4d03c686c1ff&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-22 10:35

M201608211034{
;
; Generic Julia set.
;
init:

  c =3*#pixel
  z=-2.735865250I
loop:
  z0=z
  z =(1-z^2)/(z-z^2*tan(z)) +c
  z =(1-z^2)/(z-z^2*tan(z)) +c
bailout:
  |z|<=12&&|z-z0|>=0.00003
default:
  title = " M201608211034"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\julia.html"
$IFDEF VER50
  rating = recommended
$ENDIF
param bailout
caption = "Bailout value"
default = 0.00001
min = 0.0

$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 = "Mandelbrot"
  power = power
  bailout = bailout
}

作者: 柳烟 时间: 2016-8-22 13:44

图片附件: 无标题.png (2016-8-22 13:44, 12.37 KB) / 下载次数 1423
http://inrm3d.cn/attachment.php?aid=24988&k=e2c62a729a3afcbad25f4717580bd4b2&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-22 13:54

Z的初值：3.878470957*10^(-14)-2.735865250*I
定位：1.100393960185727121433+0.2909552913983063124189 i
放大倍数：1.4076736E12

图片附件: 2.jpg (2016-8-22 19:25, 26.44 KB) / 下载次数 1441
http://inrm3d.cn/attachment.php?aid=24989&k=12f5a3175b357a956c3277836f05cd58&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-22 14:51

Z的初值：-1.162979329
定位：-0.101501271393912+0.01014084978161515 i
放大倍数：171596.15

[attach]24992[/attach]

图片附件: 3.jpg (2016-8-22 19:26, 26.54 KB) / 下载次数 1433
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图片附件: 5.jpg (2016-8-22 19:26, 26.87 KB) / 下载次数 1337
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作者: 柳烟 时间: 2016-8-22 17:03

结合maple 15与 GSP结合，用高精位点坐标工具，又算出了一个实零点：0.665299635254637，再扫一张小M集，挺漂亮的：

图片附件: 67.jpg (2016-8-22 19:27, 28.52 KB) / 下载次数 1438
http://inrm3d.cn/attachment.php?aid=24993&k=8ca975f47d0f0b9892a2cef7e9fdb90d&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-23 12:11

The Mandelbrot set for (1 - z2)/(z - z2cos(z)) + cM20160817{
;
; Generic Julia set.
;
init:

  c =3*#pixel
  z=sqrt(1.5445654699195-c)
loop:
  z0=z
  z=z^2+c
  z =(1-z^2)/(z-z^2*cos(z)) +c
  z =(1-z^2)/(z-z^2*cos(z)) +c
bailout:
  |z-z0| >= @bailout&&|z|<=12
default:
  title = "The Mandelbrot set for (1 - z2)/(z - z2cos(z)) + cM"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\julia.html"
$IFDEF VER50
  rating = recommended
$ENDIF
param bailout
caption = "Bailout value"
default = 0.00001
min = 0.0

$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 = "Mandelbrot"
  power = power
  bailout = bailout
}

作者: 柳烟 时间: 2016-8-23 12:31

定位：0.17015934857325325+-1.341987480044379e-9 i
放大：44432004

图片附件: 345.jpg (2016-8-24 08:20, 51.91 KB) / 下载次数 1648
http://inrm3d.cn/attachment.php?aid=24994&k=98d854ca2a44772fb1e1ac7df8681318&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-24 22:44

征解复分形

网络地址：https://en.wikibooks.org/wiki/Pictures_of_Julia_and_Mandelbrot_Sets/Print_Version

图片附件: rt.jpg (2016-8-28 09:21, 54.24 KB) / 下载次数 1592
http://inrm3d.cn/attachment.php?aid=24995&k=d841da557e875801d072e0d52ce428b7&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-24 22:48

网站给出的程序：
Mandelbrot {
global:
float p = 0.26  ;parameter
float deg = 4  ;degree of the polynomial
float v = 1 / log(deg)
float g = 10 * log(10)
float r = exp(g)  ;square of the radius of the bail-out circle
u = log(g)
float tb = sqr(@thick / (1000 * #magn))  ;for the thickness of the boundary
float h = 1 / (1500 * #magn * @width)  ;a very small real number
init:
complex z = 0  ;critical point
complex zd = 0  ;the sequence of the derivatives
complex z1 = 0
float w = 0
int n = 0
while n < #maxit && |z| < r
n = n + 1
z1 = z^2/2 + p*z^4
zd = ((z+h)^2/2 + p*(z+h)^4 - z1) * zd / h + 1
z = z1 + #pixel
endwhile
if n == #maxit || sqr(log(|z|)) * |z| < tb * |zd|
w = -1
else
w = n - v * (log(log(|z|)) - u)
endif
;begin fictive loop
z = 0
n = 0
loop:
n = n + 1
z = z + #pixel
if n == 1
z = w
endif
bailout:
n < 1
;end fictive loop
default:
title = "Mandelbrot"
maxiter = 100
param thick
caption = "boundary"
default = 1.0
endparam
param width
caption = "width"
default = 640
endparam
}
下面是作色算法：
Gradient {
final:
float s = real(#z)
float u = 0
if s < 0
#solid = true
else
u = (@dens * s + @disp) / 100
#index = u - trunc(u)
endif
default:
title = "Gradient"
param disp
caption = "displace"
default = 0
endparam
param dens
caption = "density"
default = 1.0
endparam
}

作者: lnszdzg100 时间: 2016-8-26 15:46

The two programs can be copied and inserted in an empty formula and colouring document, respectively. We have inserted the polynomial {\displaystyle z^{2}/2+p*z^{4}+c} {\displaystyle z^{2}/2+p*z^{4}+c} of degree 4, where p is a real parameter. The picture shows a section of the Mandelbrot set for p = 0.26.

作者: 柳烟 时间: 2016-8-26 20:40

UF中打开是黑的，说明用et调色不行了，要用其它调色法才能出现分形图形。
网上分形1000(1-z)/(8-4z+2z^2-z^3)+c的J集就是如此。

图片附件: 11111.jpg (2016-8-28 09:20, 28.84 KB) / 下载次数 1305
http://inrm3d.cn/attachment.php?aid=24996&k=6b331ad6db3ec53b422ae80d5e4e779f&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 21:38

Nova (Mandelbrot),z-f(z)/f'(z)+c应定位于z-f(z)/f'(z)+c的导函数为零的点，这样才能扫出标准的M集。

这是f(z)=z^3-1的此种分形。
NovaMandel {
init:

z = 1

loop:
zold=z
z = z - (z^3-1) / (3*z^2) + #pixel

bailout:
  |z - zold| > @bailout

default:
  title = "Nova (Mandelbrot)"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\nova.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  maxiter = 1000
  periodicity = 0
  center = (-0.5,0)
  magn = 1.5

  param bailout
caption = "Bailout"
default = 0.00001
$IFDEF VER40
exponential = true
$ENDIF
hint = "Bailout value; smaller values will cause more \
         iterations to be done for each point."
  endparam

switch:
  type = "NovaJulia"
  seed = #pixel
  power = @power
  bailout = @bailout
  relax = @relax
}

图片附件: Fractal3.png (2016-8-27 21:38, 44.41 KB) / 下载次数 1261
http://inrm3d.cn/attachment.php?aid=24997&k=f7f1e8f50380dceb458f677c723bded3&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 21:49

有三种定位法

图片附件: 定位.jpg (2016-8-27 21:49, 19.91 KB) / 下载次数 1235
http://inrm3d.cn/attachment.php?aid=24998&k=3415fa9458cac06abd01daf8eca8d591&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 22:03

好象也可定位为f(z)的零点，我正在UF中尝试，大家可研究看看。

作者: 柳烟 时间: 2016-8-27 22:10

NovaMandel {
init:
z =sqrt(1-#pixel)
loop:
z=z^2+#pixel
zold=z
z = z - (z^3-1) / (3*z^2) + #pixel
bailout:
  |z - zold| > @bailout

default:
  title = "Nova (Mandelbrot)"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\nova.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  maxiter = 1000
  periodicity = 0
  center = (-0.5,0)
  magn = 1.5

  param bailout
caption = "Bailout"
default = 0.00001
$IFDEF VER40
exponential = true
$ENDIF
hint = "Bailout value; smaller values will cause more \
         iterations to be done for each point."
  endparam

switch:
  type = "NovaJulia"
  seed = #pixel
  power = @power
  bailout = @bailout
  relax = @relax
}
此是复合函数，定位于z=0或者z=sqrt(1-c)或z=-sqrt(1-c)或者z=sqrt(－0.5-.866025403784439I-c)或者z=sqrt(－0.5-.866025403784439I-c)

作者: 柳烟 时间: 2016-8-27 22:13

定位于z=0的情形

图片附件: 1.png (2016-8-27 22:13, 17.45 KB) / 下载次数 1200
http://inrm3d.cn/attachment.php?aid=24999&k=5a902a055f1a2d32aa79bb6234e9ae74&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 22:15

定位于z=sqrt(1-c)

图片附件: 2.png (2016-8-27 22:15, 16.25 KB) / 下载次数 1214
http://inrm3d.cn/attachment.php?aid=25000&k=d0eb45c74615d228b58fd2a7f6ceae96&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 22:25

定位于z=sqrt(－0.5-.866025403784439I-c)

图片附件: 3.png (2016-8-27 22:25, 15.82 KB) / 下载次数 1205
http://inrm3d.cn/attachment.php?aid=25001&k=16c7815902d272669a85420987dfe068&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 22:57

这是大家熟悉的N集：
Mandel {
init:
z=sqrt(1/6*(#pixel^2+1))
loop:
zold=z
z = z - (z^2-1)*(z^2-#pixel^2) /(4*z^3-2*(#pixel^2+1)*z)
bailout:
  |z - zold| > @bailout

default:
  title = "Nova (Mandelbrot)"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\nova.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  maxiter = 1000
  periodicity = 0
  center = (0,0)
  magn = 1.5

  param bailout
caption = "Bailout"
default = 0.00001
$IFDEF VER40
exponential = true
$ENDIF
hint = "Bailout value; smaller values will cause more \
         iterations to be done for each point."
  endparam

switch:
  type = "NovaJulia"
  seed = #pixel
  power = @power
  bailout = @bailout
  relax = @relax
}

图片附件: 4.png (2016-8-27 22:57, 31.1 KB) / 下载次数 1132
http://inrm3d.cn/attachment.php?aid=25002&k=28a0bf79f1afd6c11959e0f5b76e3d74&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 23:00

将上楼按NovaMandel分形造之，令（z^2-1）(z^2-c^2)=0,得z=1或-1,z=c或z=-c，放大后，均可得小M。
定位于z=1,效果图如下

定位于z=c.得：

图片附件: 6.jpg (2016-8-28 09:18, 23.13 KB) / 下载次数 1177
http://inrm3d.cn/attachment.php?aid=25003&k=61ab9978a8836a69af7ba4f4eab9044f&t=1732400877&sid=QqS2X2

图片附件: 8.jpg (2016-8-28 09:18, 48.6 KB) / 下载次数 1170
http://inrm3d.cn/attachment.php?aid=25004&k=422d66303f6effdf6f3287b361f7cb6f&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 23:21

此类分形确实漂亮，再扫一个：

图片附件: 12.jpg (2016-8-28 09:18, 34.01 KB) / 下载次数 1142
http://inrm3d.cn/attachment.php?aid=25006&k=7448b17c2abfb6c95b37c455fe7fef69&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-27 23:54

扫得一美图：定位：-0.1962680668423+0.039689218342819 I
放大倍数：34984.675

附UF程序：
NovaMandel {
init:
z=1
loop:
zold=z
z = z - (z^2-1)*(z^2-#pixel^2) /(4*z^3-2*(#pixel^2+1)*z)  + #pixel
bailout:
  |z - zold| > @bailout

default:
  title = "Nova (Mandelbrot)"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\nova.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  maxiter = 1000
  periodicity = 0
  center = (0,0)
  magn = 1.5

  param bailout
caption = "Bailout"
default = 0.00001
$IFDEF VER40
exponential = true
$ENDIF
hint = "Bailout value; smaller values will cause more \
         iterations to be done for each point."
  endparam

switch:
  type = "NovaJulia"
  seed = #pixel
  power = @power
  bailout = @bailout
  relax = @relax
}
GSP中扫一张

20168290125M.gsp (15.83 KB)

图片附件: 13.jpg (2016-8-28 09:19, 34.85 KB) / 下载次数 1164
http://inrm3d.cn/attachment.php?aid=25007&k=d9a72acf0c2cf019948f71f4da819fda&t=1732400877&sid=QqS2X2

图片附件: 4.jpg (2016-8-29 20:38, 47.06 KB) / 下载次数 1138
http://inrm3d.cn/attachment.php?aid=25008&k=e81486ec89c9e2baab56c3579c79e38e&t=1732400877&sid=QqS2X2

附件: 20168290125M.gsp (2016-8-29 01:26, 15.83 KB) / 下载次数 2461
http://inrm3d.cn/attachment.php?aid=25009&k=752edb73e491fe15dd5cfb31d7a1f18a&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-29 12:47

201608291107NovaMandel {
init:
c=1/(5*#pixel)
   z=c
loop:

   zold=z
   z = z - (z^2-1)*(z^2-c^2) /(4*z^3-2*(c^2+1)*z)  + c
   bailout:
  |z-zold|>=@bailout

default:
  title = "201608291107NovaMandelNova (Mandelbrot)"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\nova.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  maxiter = 1000
  periodicity = 0
  center = (0,0)
  magn = 1.5
  param bailout
caption = "Bailout"
default = 0.00001
$IFDEF VER40
exponential = true
$ENDIF
hint = "Bailout value; smaller values will cause more \
         iterations to be done for each point."
  endparam
}

定位：-0.546532667247111135675+0.0027467262320658779639 I
放大倍数：1.4394026E10

图片附件: 829.jpg (2016-8-29 20:40, 50.8 KB) / 下载次数 1170
http://inrm3d.cn/attachment.php?aid=25010&k=980d2e3821a81ae03f8e510400714524&t=1732400877&sid=QqS2X2

图片附件: 90.jpg (2016-8-29 20:40, 22.75 KB) / 下载次数 969
http://inrm3d.cn/attachment.php?aid=25011&k=1cb01c2b3408d15fec7f22ac7d0878c2&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-29 20:59

201608292056NovaMandel {
init:
c=#pixel
z=asin(c)
loop:
  zold=z
  z = z - (sin(z)-c) /cos(z)+c
bailout:
  |z-zold|>=@bailout
default:
  title = "201608292056NovaMandelNova (Mandelbrot)"
  helpfile = "Uf*.chm"
  helptopic = "Html\formulas\standard\nova.html"
$IFDEF VER50
  rating = recommended
$ENDIF
  maxiter = 1000
  periodicity = 0
  center = (0,0)
  magn = 1.5
  param bailout
caption = "Bailout"
default = 0.00001
$IFDEF VER40
exponential = true
$ENDIF
hint = "Bailout value; smaller values will cause more \
         iterations to be done for each point."
  endparam
}
定位：0.727105830556525+0.0014871720962649 I
放大倍数：46776.449

图片附件: Fractal2.jpg (2016-8-29 21:55, 34.07 KB) / 下载次数 1071
http://inrm3d.cn/attachment.php?aid=25012&k=2c63757f2a604fcbf65e002d56564bdd&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-8-29 23:31

图片附件: 91.jpg (2016-11-10 10:54, 22.66 KB) / 下载次数 1086
http://inrm3d.cn/attachment.php?aid=25013&k=0eaedc1c6eea5806bb26b20d2ac3c2f4&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-10-2 22:53

图片附件: 2.jpg (2016-11-10 10:55, 21.14 KB) / 下载次数 1063
http://inrm3d.cn/attachment.php?aid=25020&k=e06cb99fcd18c1f1ec1a41cf51992a45&t=1732400877&sid=QqS2X2

图片附件: 3.jpg (2016-11-10 10:55, 25.11 KB) / 下载次数 1109
http://inrm3d.cn/attachment.php?aid=25021&k=02c8f4594571a267d4f3d020dc820f55&t=1732400877&sid=QqS2X2

作者: 柳烟 时间: 2016-10-3 22:17

gnd-MandelJulia.gsp (15.1 KB)

附件: gnd-MandelJulia.gsp (2016-10-3 22:17, 15.1 KB) / 下载次数 2287
http://inrm3d.cn/attachment.php?aid=25022&k=04d67cda781e909ec4cd8f06221b37ba&t=1732400877&sid=QqS2X2

作者: lnszdzg100 时间: 2016-11-4 14:46

问柳老师好，画板论坛最近很少有人来了，太可惜了1

作者: lnszdzg100 时间: 2016-11-4 15:51

将+c改成-c，就这样美1

图片附件: 捕获1.jpg (2016-11-10 10:53, 41.2 KB) / 下载次数 1875
http://inrm3d.cn/attachment.php?aid=25024&k=f72c839386ae3b4aaf33b74d5bd2d2e5&t=1732400877&sid=QqS2X2

图片附件: 捕获2.jpg (2016-11-10 10:53, 13.32 KB) / 下载次数 1860
http://inrm3d.cn/attachment.php?aid=25025&k=bb68592633ccc967dee0cb850e105ec9&t=1732400877&sid=QqS2X2

图片附件: 捕获3.jpg (2016-11-10 10:53, 29.87 KB) / 下载次数 1842
http://inrm3d.cn/attachment.php?aid=25026&k=b92a91c0d68a66b644ef47c1c2ca7efa&t=1732400877&sid=QqS2X2

图片附件: 捕获4.jpg (2016-11-10 10:53, 38.08 KB) / 下载次数 1854
http://inrm3d.cn/attachment.php?aid=25027&k=fb1b8b6b388ce94118c1d693a45a7ccc&t=1732400877&sid=QqS2X2

图片附件: 捕获5.jpg (2016-11-10 10:53, 59.7 KB) / 下载次数 2019
http://inrm3d.cn/attachment.php?aid=25028&k=ff60c037b254ac12f88a39ea0f686ba7&t=1732400877&sid=QqS2X2

作者: lnszdzg100 时间: 2016-11-4 19:31

找了一个双核的

图片附件: 捕获6.jpg (2016-11-10 10:48, 18.94 KB) / 下载次数 1972
http://inrm3d.cn/attachment.php?aid=25029&k=7917714aad27465c9c12b26f58210065&t=1732400877&sid=QqS2X2

作者: lnszdzg100 时间: 2016-11-5 21:59

这个的陷阱该如何做？

图片附件: 捕获7.jpg (2016-11-10 10:48, 29.84 KB) / 下载次数 1909
http://inrm3d.cn/attachment.php?aid=25031&k=14f64568004f950e507db33f3977fd36&t=1732400877&sid=QqS2X2

作者: xiaongxp 时间: 2016-11-6 09:27

这是六圆极限集[42]，可参考《…50例》中例44的八圆极限集[44]作。但不加陷阱按内迭代法(例39方法)作成上楼样式更漂亮。

作者: lnszdzg100 时间: 2016-11-9 10:02

树被活活砍断了，我没法修复啊！

图片附件: 20161109001.jpg (2016-11-10 10:46, 27.17 KB) / 下载次数 2033
http://inrm3d.cn/attachment.php?aid=25034&k=7144ce22ae1e04745a2f1b2693aac02b&t=1732400877&sid=QqS2X2

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