位于sam.ufm系列中的科赫雪花曲线，我看了，扫描法出来的图形，美。我正在造第一个开关项，觉得这开关项可能简单点，单就这开关项的程序还没完全懂，我感觉到此分形能用几何画板做。
KochCurve {
; By Samuel Monnier, 2.1.00
init:
z = #pixel
zz = 0
; Twist
z = 1/sqrt(@r)*real(z) + 1i*sqrt(@r)*imag(z)
x = real(z)
y = imag(z)
sq3 = sqrt(3)
bool bail2 = false
bool bail = false
i = 0
loop:
i = i + 1
;----------------
; First Iteration
;----------------
if i == 2
; Calculate the argument of z
arg = atan2(z)
; Inside approximation
if @region == 0 || @region == 2
; Draw the Star of David
if (y + 1/sq3 > 0) && (sq3*x - y + 2/sq3 > 0) \
&& (sq3*x + y - 2/sq3 < 0)
bail = true
endif
if (-y + 1/sq3 > 0) && (sq3*x + y + 2/sq3 > 0) \
&& (sq3*x - y - 2/sq3 < 0)
bail = true
endif
; Deal the case where z needs a rotation
if (arg > 5/6*pi) || (arg < -pi/2)
z = z*exp(1i*4/3*pi)
endif
if (arg < pi/6) && (arg > -pi/2)
z = z*exp(1i*2/3*pi)
endif
z = z - 1i*1/sq3
if @region == 2
zz = z
z = #pixel
endif
endif
; Outside approximation
if @region == 1 || @region == 2
; Draw the hexagon
if |x| > 1 || x/sq3 + y - 2*sq3/3 > 0 \
|| x/sq3 + y + 2*sq3/3 < 0 || x/sq3 \
- y + 2*sq3/3 < 0 || x/sq3 - y - \
2*sq3/3 > 0
bail = true
endif
; Deal the case where z needs a rotation
if (abs(arg) < pi/6)
z = z*exp(-1i*pi/2)
elseif (arg > pi/6) && (arg < pi/2)
z = z*exp(-1i*5*pi/6)
elseif (arg > pi/2) && (arg < 5*pi/6)
z = z*exp(1i*5*pi/6)
elseif (abs(arg) > 5*pi/6)
z = z*exp(1i*pi/2)
elseif (arg < -pi/6) && (arg > -pi/2)
z = z*exp(-1i*pi/6)
elseif (arg < -pi/2) && (arg > -5*pi/6)
z = z*exp(1i*pi/6)
endif
z = z + 1i
z = sq3*z
endif
;----------------
;Other Iterations
;----------------
elseif i > 2
; "Undo" the offset parameter's
; action
z = z + @offset
z = 1/sqrt(@r)*real(z) + 1i*sqrt(@r)*imag(z)
if @region == 2
oldz = z
z = zz
zz = oldz
endif
; Magnify z so that a simple formula
; allows to compute...
z = 3*z
x = real(z)
y = imag(z)
; ...the new triangle on the segment
if (y > 0) && (sq3*x - y + sq3 > 0) \
&& (sq3*x + y - sq3 < 0)
bail2 = true
endif
; Restore the original value of z
z = z/3
x = real(z)
y = imag(z)
; Transforms the left segment
if x < -1/3
z = 3*z + 2
; Transforms the right segment
elseif x > 1/3
z = 3*z - 2
else
; Transforms the middle-left segment
if x < 0
z = z + 1/3
z = z*exp(-1i*pi/3)
z = 3*z - 1
; Transforms the middle-right segment
else
z = z - 1/3
z = z*exp(1i*pi/3)
z = 3*z + 1
endif
endif
endif
; A parameter to fool some coloring
; algorythms like final decomposition...
if i >= 2
z = z - @offset
endif
bailout:
bail == false && bail2 == false
default:
title = "Koch Curve"
helpfile = "sam-help/kochcurves.htm"
helptopic = "kcurve"
magn = 1.5
center = (0.0002,0)
maxiter = 50
param region
caption = "Trapped Region"
default = 0
enum = "Inside" "Outside" "Both"
endparam
param offset
caption = "Offset"
default = (0,0)
endparam
param r
caption = "Twist Parameter"
default = (1,0)
endparam
} |
