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无标题.png
2016-8-22 13:44
静极光通达,寂照含虚空,
Z的初值:3.878470957*10^(-14)-2.735865250*I
定位:1.100393960185727121433+0.2909552913983063124189 i
放大倍数:1.4076736E12
2.jpg
2016-8-22 19:25
静极光通达,寂照含虚空,
Z的初值:-1.162979329
定位:-0.101501271393912+0.01014084978161515 i
放大倍数:171596.15
3.jpg
2016-8-22 19:26

[attach]24992[/attach]
5.jpg
静极光通达,寂照含虚空,
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:
67.jpg
2016-8-22 19:27
静极光通达,寂照含虚空,
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
}
静极光通达,寂照含虚空,
定位:0.17015934857325325+-1.341987480044379e-9 i
放大:44432004
345.jpg
2016-8-24 08:20
静极光通达,寂照含虚空,
静极光通达,寂照含虚空,
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
}
静极光通达,寂照含虚空,
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。
11111.jpg
2016-8-28 09:20
静极光通达,寂照含虚空,
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。
Fractal3.png
2016-8-27 21:38

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
}
静极光通达,寂照含虚空,
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