# 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
```