柳烟

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
}

lnszdzg100

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.

柳烟

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。

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2016-8-28 09:20

柳烟

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。

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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
}

柳烟

有三种定位法

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2016-8-27 21:49

柳烟

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。

柳烟

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)

柳烟

定位于z=0的情形

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2016-8-27 22:13

柳烟

定位于z=sqrt(1-c)

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2016-8-27 22:15

柳烟

定位于z=sqrt(－0.5-.866025403784439I-c)

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2016-8-27 22:25