Fractals : Von Koch snowflake - Printable Version

Fractals : Von Koch snowflake - Printable Version

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Fractals : Von Koch snowflake - Damien - 12-11-2013 11:08 PM

Hi everyone,

This small program draws some simple fractals.
The K parameter controls the curve complexity.
Change K value from 0 (3 segments drawn), to 6 (12288 segments drawn).

Code:

EXPORT VON_KOCH_SNOWFLAKES()

BEGIN

 LOCAL T2,T1,AA,LL,a,l,L0;

 LOCAL Xi,Yi,X1,Y1,X0,Y0;

 LOCAL XA,YA,XD,YD,A0,II;

 LOCAL x,y,NP;

// Init parameters

 HAngle:=0; // RAD

 M:=3;

 N:=4;

 K:=5; // change K from 0 to 6 (or 7 if you are very very... patient)

 NP:=208;

// Point coordinates of the starting curve

 x:={0,NP,NP/2,0};

 y:={√3/2*NP,√3/2*NP,0,√3/2*NP};

// Model segments Length

 l:={1/3,1/3,1/3,1/3};

// Segments angle with the horizontal

 a:={0,π/3,−π/3,0};

// Black screen

 RECT_P(#383838h);

// Main loop 

 FOR II:=1 TO M DO

// Calculate starting and ending point of segment number II

  XD:=x(II); YD:=y(II);

  XA:=x(II+1); YA:=y(II+1);

  X0:=XD; Y0:=YD;

  IF XA<>XD THEN 

   A0:=ATAN((YA−YD)/(XA−XD)) ;

  ELSE 

   A0:=π/2*SIGN(YA−YD); 

  END;

  IF (XA−XD)<0 THEN A0:=A0+π; END;

  L0:=√((XA−XD)²+(YA−YD)²);

// Move the pen to its starting place

  Xi:=IP(X0); Yi:=IP(Y0);

//secondary loop: each time it pass through, an elementary segment is plotted.

  FOR I:=0 TO N^K−1 DO // so there is  N^K segments to draw (M time)

   LL:=L0; AA:=A0 ; T1:=I;

    IF K<>0 THEN 

     FOR J:=K−1 DOWNTO 0 STEP 1 DO

      R:=N^J; T2:=IP(T1/R);

      AA:=AA+a(T2+1); // angle for segment number I

      LL:= LL*l(T2+1); // length for segment number I 

      T1:=T1−T2*R;

     END; // NEXT J

    END;

// Time to draw

    X0:=X0+LL*COS(AA); 

    Y0:=Y0+LL*SIN(AA);

    X1:=IP(X0); Y1:=IP(Y0);

    LINE_P(Xi,Yi,X1,Y1,RGB(240,230,0)); // orange

    Xi:=X1; Yi:=Y1;

   END; // NEXT I

  END; // NEXT II

  WAIT(-1);

END;

Now if you want the fractal to grow inside the triangle replace the line:

Code:

x:={0,NP,NP/2,NP}

with:

Code:

x:={NP,0,NP/2,NP}

and you've got another variant of the Von Koch snowflake.

For something a little different, you can remplace the init parameters with:

Code:

 M:=4; N:=4; K:=5;

 NP:=208;

 x:={0,NP,NP,0,0};

 y:={0,0,NP,NP,0};

 l:={1/(2+2*COS(.45*π)),1/(2+2*COS(.45*π)),1/(2+2*COS(.45*π)),1/(2+2*COS(.45*π))};

 a:={0,.45*π,−.45*π,0};

Code:

 M:=4; N:=4; K:=6;

 NP:=208;

 x:={0,NP,NP,0,0};

 y:={0,0,NP,NP,0};

 l:={1/(2+2*COS(.48*π)),1/(2+2*COS(.48*π)),1/(2+2*COS(.48*π)),1/(2+2*COS(.48*π))};

 a:={0,.48*π,−.48*π,0};

Code:

 M:=1; N:=4; K:=6;

 NP:=208;

 x:={0,0};

 y:={NP,-NP};

 l:={1/3,1/3,√10/9,5/9};

 a:={0,π/2,−ATAN(3),0};

Or (added 15/12/2013)

Code:

 M:=2; N:=2; K:=12;

 NP:=240;

 x:={NP/2,NP/2,NP/2};

 y:={NP/4,3*NP/4,NP/4};

 l:={1/√2,1/√2};

 a:={π/4,−π/4)};

(added 16/12/2013)
Now lets try to cut corners. The segments drawing will now be replaced by arcs of ellipse.
The basic program is the same, with only the addition of few extra lines of code.
The S parameter controls the smoothness of the rounding, the K parameter controls the complexity degree of the curve.

Code:

EXPORT Rounded_Fractal()

BEGIN

LOCAL T2,T1,AA,LL,a,l,L0;

LOCAL Xi,Yi,X1,Y1,X0,Y0;

LOCAL XA,YA,XD,YD,A0,II;

LOCAL x,y,NP,X2,Y2,VX,VY;

LOCAL WX,WY,K4,XQ,YQ,AN;

HAngle:=0; // RAD 

// init parameters

 M:=2; N:=4; K:=6; S:=3;

 NP:=240;

 x:={0,NP,0};

 y:={NP,0,NP};

 l:={1/2,.45,.45,.5};

 a:={0,π/2,−π/2,0};

// Clear screen

 RECT_P(#383838h);

// main loop 

 FOR II:=1 TO M DO

  XD:=x(II); YD:=y(II);

  XA:=x(II+1); YA:=y(II+1);

  X0:=XD; Y0:=YD; X1:=X0; Y1:=Y0;

  X2:=X0; Y2:=Y0; 

   IF XA<>XD THEN 

   A0:=ATAN((YA−YD)/(XA−XD)) ;

  ELSE 

   A0:=π/2*SIGN(YA−YD); 

  END;

  IF (XA−XD)<0 THEN A0:=A0+π; END;

   L0:=√((XA−XD)²+(YA−YD)²);

   FOR I:=0 TO N^K−1 DO

    LL:=L0; AA:=A0 ; T1:=I;

    IF K<>0 THEN 

     FOR J:=K−1 DOWNTO 0 STEP 1 DO

      R:=N^J; T2:=IP(T1/R);

      AA:=AA+a(T2+1); LL:= LL*l(T2+1);

      T1:=T1−T2*R;

     END; // NEXT J

    END;

    X0:=X1; Y0:=Y1; X1:=X2; Y1:=Y2;

    X2:=X2+LL*COS(AA);Y2:=Y2+LL*SIN(AA);

    VX:=X1-X0; VY:=Y1-Y0;

    WX:=X2-X1; WY:=Y2-Y1; 

    FOR K4:=0 TO S DO

     AN:=π/2*K4/S;

     XQ:=(X0+X2-COS(AN)*WX+SIN(AN)*VX)/2;

     YQ:=(Y0+Y2-COS(AN)*WY+SIN(AN)*VY)/2;

     IF I==0 THEN  

      Xi:=IP(X0); Yi:=IP(Y0);

     END;

     IF I>0 THEN

      LINE_P(Xi,Yi,IP(XQ),IP(YQ),RGB(240,230,0)); 

      Xi:=IP(XQ); Yi:=IP(YQ); 

    END;

   END; // NEXT K4

  END; // NEXT I

 END; // NEXT II

 WAIT(-1);

END;

(added 18/12/13)
Lets change some init parameters like so:

Code:

 M:=1; N:=13; K:=3; S:=4;

 NP:=240;

 x:={0,NP};

 y:={NP,0};

 l:={.4,.4,.2,.2,.2,.2,.4,.4,.2,.2,.2,.2,.2};

 a:={0,π/2,0,−π/2,0,−π/2,-π,−π/2,0,π/2,0,π/2,0};

Cheers,

Damien.

RE: Fractales : Von Koch snowflake - ArielPalazzesi - 12-14-2013 09:03 PM

Downloading...... Wink

Thanks!

RE: Fractals : Von Koch snowflake - Damien - 12-14-2013 11:01 PM

You're welcome ! Have Fun !

regards,

Damien.

RE: Fractales : Von Koch snowflake - Mic - 12-15-2013 06:14 PM

Nice work !

RE: Fractals : Von Koch snowflake - Damien - 12-15-2013 07:07 PM

And more to come very soon!

Cheers,

Damien.