LOGO-L> Seirpinski's Carpet

["John Hayes" <jahayes@xtra.co.nz>]

V Jones (19/8/98) has produced a beautiful fractal in his Seirpinski's
Carpet program. I have taken the liberty of modifying and expanding the
sq_seirp procedure in order to make the program into a microworld
user-friendly for children 9 years and older. They aim is that they have 
access to the beauty of the fractals produced, and that induction of the
pattern of the fractals as the levels deepen is facilitated. 

The enhancements I have added are the placing of the fractals produced
side-by-side so that they can be compared, and the printing to the graphics
screen of a label for each fractal stating its level of recursion. I
envisage the teacher challenging the students to be systematic as they
enter numbers so that a pattern they can study will emerge.

TO S
     WINDOW CS SETPC BLACK
     SETFONT 'System' 10 1
     PU SETXY [-300 -75] PD CT
     PPR 'Input the side length (about 70) and press Enter,'
     PPR 'then input the recursion level (a number less than 7 works
best).'
     MAKE "SIDE READ
     MAKE "LEVEL READ
     IF :LEVEL > 2 THEN HT
     CARPET :SIDE :LEVEL
     CARPETFILL :SIDE :LEVEL
     PU SETY -85 PD SETPC BLACK TT (SE 'level' :LEVEL) PU SETY -75 PD
     CT SS PR 'Would you like to try a different recursion level? Y or N.'
     MAKE "CHOICE READ
     IF :CHOICE = "Y THEN RUN.IT.AGAIN ELSE CT PR 'Goodbye for now.'
TOPLEVEL
END

TO RUN.IT.AGAIN
     CT ST SETPC BLACK PPR 'Enter a new recursion level.'
     MAKE "LEVEL READ
     IF :LEVEL > 2 THEN HT
     PU RT 90 FD :SIDE + 20 PD LT 90
     CARPET :SIDE :LEVEL
     CARPETFILL :SIDE :LEVEL
     PU SETY -85 PD SETPC BLACK TT (SE 'level' :LEVEL) PU SETY -75 PD
     CT SS PR 'Would you like to try a different recursion level? Y or N.'
     MAKE "CHOICE READ
     IF :CHOICE = "Y THEN RUN.IT.AGAIN ELSE CT PR 'Goodbye for now.'
TOPLEVEL
END

TO CARPET :SIDE :LEVEL
     IF :LEVEL < 1 [STOP]
     REPEAT 4 [CARPET :SIDE / 3 :LEVEL - 1 FD :SIDE / 3 CARPET :SIDE / 3
:LEVEL - 1 FD 2 * :SIDE / 3 RT 90]
END

TO CARPETFILL :SIDE :LEVEL
     IF :LEVEL < 2 [STOP]
     IF :LEVEL = 2 [SETPC 9]
     IF :LEVEL = 3 [SETPC 12]
     IF :LEVEL = 4 [SETPC 10]
     IF :LEVEL = 5 [SETPC 14]
     PU RT 45 FD 2 * (:SIDE / 3) PD FILL PU BK 2 * (:SIDE / 3) LT 45
     FD :SIDE / 3
     CARPETFILL :SIDE / 3 :LEVEL - 1
     FD :SIDE / 3
     CARPETFILL :SIDE / 3 :LEVEL - 1
     FD :SIDE / 3 RT 90 FD :SIDE / 3
     CARPETFILL :SIDE / 3 :LEVEL - 1
     FD :SIDE / 3
     CARPETFILL :SIDE / 3 :LEVEL - 1
     FD :SIDE / 3 RT 90 FD :SIDE / 3
     CARPETFILL :SIDE / 3 :LEVEL - 1
     FD :SIDE / 3
     CARPETFILL :SIDE / 3 :LEVEL - 1
     FD :SIDE / 3 RT 90 FD :SIDE / 3
     CARPETFILL :SIDE / 3 :LEVEL - 1
     FD :SIDE / 3
     FD :SIDE / 3 RT 90
     CARPETFILL :SIDE / 3 :LEVEL - 1
END

John Hayes
Te Puke Primary School
NEW ZEALAND


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