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• ## A new mixed IFS type of space filling curve:

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• I used an irrational rotational square as one of the IFS transforms: this mixes chaos, number theory and fractal theory in one program. I use my Ulam
Message 1 of 1 , Jul 1, 2002
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I used an irrational rotational square as one of the IFS transforms:
this mixes chaos, number theory and fractal theory in one program.
I use my Ulam differential curvature monitor to show the difference
in the types and the patterns inside the space filling curve.
Respectfully, Roger L. Bagula
619-5610814 :
TFTN web sites maintained as an Emag:
URL : http://victorian.fortunecity.com/carmelita/435/
URL : http://www.crosswinds.net/~translight/index.html

True basic program:
SET MODE "color"
SET WINDOW 0,1922,0,1062
SET BACKGROUND COLOR "white"
LET x=0
LET y=0
LET a=0
LET b =0
LET s1=400
LET s2 =s1*1062/1922
RANDOMIZE
PRINT" SQUARE 4 TRANSFORMS I.F.S. MIXED IRRATIONAL ROTATION"
PRINT" BY R.L.BAGULA 1 July 2002 © "
FOR n= 1 TO 8000000
LET a =RND
LET r=2
IF a <= 1/4 THEN
LET x1=X/r+1
LET y1=Y/r+1
REM SET COLOR "BLUE"
END IF
IF a<= 2/4 AND a>1/4 THEN
LET x1=X/r-1
LET y1=Y/r-1
REM SET COLOR "RED"
END IF
IF a<= 3/4 AND a>2/4 THEN
LET x1=X/r-1
LET y1=Y/r+1
REM SET COLOR "MAGENTA"
END IF
IF a<= 1 AND a>3/4 THEN
LET x1=2*MOD(PI*N,1)
LET y1=2*MOD(EXP(1)*N,1)-2
REM SET COLOR "BLACK"
END IF

REM color monitor calculation
LET x30=x2
LET y30=y2
LET x2=x
LET y2=y
LET x=x1
LET y=y1
REM first derivative
LET dx1=x2-x+.001
LET dy1=y2-y
REM second derivative
LET dx2=x2-2*x+x30
LET dy2=y2-2*y+y30
REM Gaussian curvature
LET k0=(dx1*dy2-dy1*dx2)/(dx1^2+dy1^2)^1.5

SET COLOR 32+abs((255-32)*k0)

IF n>10 THEN PLOT 1922/2+s1*x,1062/2+s2*y
NEXT n
END
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