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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
}
静极光通达,寂照含虚空,
Zwv.jpg
2016-8-20 08:04

(1-z^2)除以(z-z^2cosz)的M集20160818.gsp (20.98 KB)
无标题1.jpg
2016-8-20 08:04
静极光通达,寂照含虚空,
定位:-0.478228114006905+0.049932680209967 i
放大倍数:84047.09100
14.jpg
2016-8-20 08:02

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
45.jpg
2016-8-20 08:02
静极光通达,寂照含虚空,
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
}
Fractal3.jpg
2016-8-20 08:00

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。
静极光通达,寂照含虚空,
定位:-0.130922182998915-3.200985271711e-6 i
放大倍数:19790.037   
12.jpg
2016-8-20 07:59

201608191401M集.gsp (16.81 KB)
定位:0.419639209432235+ 0.14004931643909  i
放大倍数:19790.037
13.jpg
2016-8-20 07:59
静极光通达,寂照含虚空,
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
}
静极光通达,寂照含虚空,
定位:0.44136818689914+0.136526563444065 i
放大倍数:9558.8151
3.jpg
2016-8-20 07:57
静极光通达,寂照含虚空,
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:
复要.jpg
2016-8-19 23:16

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。
静极光通达,寂照含虚空,
34.jpg
2016-8-20 07:56

代码中的|z|<=13中的13改为8
11.jpg
2016-8-20 07:56

M20160819200042.gsp (16.9 KB)
静极光通达,寂照含虚空,
98.jpg
2016-8-20 07:53

97.jpg
2016-8-20 07:53
静极光通达,寂照含虚空,
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