pretty result from my von Koch expertiments

From: Roger L. Bagula (rlbtftn_at_netscape.net)
Date: 07/23/04


Date: Fri, 23 Jul 2004 08:26:48 GMT


It uses a partial Gauss map to curve the fractal around.
True basic:
SET MODE "color"
SET WINDOW 0,1920,0,1024
SET BACKGROUND COLOR "white"
DECLARE DEF bis4
LET x=.2
LET y=.3
LET a=0
LET b =0
LET s1=1000
LET s2 =s1*1024/1920
RANDOMIZE
LET z=rnd
PRINT" Circle Cantor set I.F.S. three parts self similar "
PRINT" in a Besicovitch -Ursell von Koch function"
PRINT" BY R.L.BAGULA 23 July 2004 ©"
PRINT" The result is von Koch gaussian map"
FOR n= 1 TO 1000000
     LET a =RND
     REM Cantor angular set
     IF a <= 1/3 THEN
        LET z1=z/3
        SET COLOR "blue"
     END IF
     IF a<= 2/3 AND a>1/3 THEN
        LET z1=z/3+1/3
        SET COLOR "black"
     END IF
     IF a<= 1 AND a>2/3 THEN
        LET z1=z/3+2/3
        SET COLOR "red"
     END IF
     LET z=z1
     REM a Besicovitch -Ursell Cantor function used instead of sine and
cosine
     IF rnd>0.5 then
        LET x1=x/3+bis4(z)
        LET y1=y/3+bis4(z+1/2)
     ELSE
        LET x1=x/3-bis4(z+1/2)
        LET y1=y/3+bis4(z)
        REM mirror transform
     END IF
     LET x=x1
     LET y=y1
     REM Gaussian map conformal projection
     LET r=sqr(x^2+y^2)
     IF n>10 THEN PLOT 1920/2+s1*x/(1+r^2),1024/2+s2*(1-r^2)/(1+r^2)-100
NEXT n
END
EXTERNAL
DEF bis4(x)
     REM Mandelbrot Multifractal cartoon function of FOUR lines defined
     REM 0<x1<x2< x3<X4=1
     REM
     REM unit square domain
     REM lines continious
     REM page 33 of "Multifractal and 1/f Noise"
     LET x0=0
     LET x1=1/3
     LET x2=1/2
     LET x3=2/3
     LET x4=1
     LET x= mod(x,1)
     IF x >= X0 and x <= x1 then LET y=0
     IF x > x1 and x <= x2 then LET y=3*sqr(3)*X-sqr(3)
     IF x > x2 and x <= x3 then LET y=-3*sqr(3)*X+2*Sqr(3)
     IF x > x3 and x <= x4 then LET y=0
     LET BIS4 =y

END DEF

Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel:
619-5610814 :
URL : http://home.earthlink.net/~tftn
URL : http://victorian.fortunecity.com/carmelita/435/




CC_VK_GAUSS_MAP.gif

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