Re: LOGO-L> hilbert again

["Olga Tuzova" <olgatu@ort.spb.ru>]

Hello everybody,

The recent posts on hilbert (sierpinski?) curves were focused on the 
algorithms design. But I think they are touching also very important 
things to which young students might be introduced in a form, 
understandable for them. I mean mapping one set onto another.

Here is a challenge for them. (Sorry, if the terminology isn't 
perfect)

Given two line segments, one is very large, the other is very short. 
Where there are more points?

I've never heard two different answers and always it's a great 
surprise for them when they are coming to the right answer by mapping 
one segment onto another (see attachment).
Imho, it's important for the kids' to understand, that to compare 
two sets you needn't always count their elements and that you may 
compare them even when you can't count elements and decide which is 
"larger" or "smaller".

And in this  context I find "Wirth's algorithm" is worth paying 
attention to, though being reproduced in logo it looks clumsy and 
there are much more elegant and efficient ones. "Wirth's algorithm" 
is very clear and some of my 13 year students (not all of course) 
could program it in logo for one of hilbert (sierpinski?) curve 
modification. I'm including it here, though the curve itself looks 
very much alike Andrzej and ... sorry, there was no name in the 
letter... showed us. BTW, Andrzej, why do you call it W-curve?
 
The problem is, I can't find the method of changing size parameter to 
make the line  always stay inside a square while filling it.

Any comments will be appreciated.

Regards,
Olga.

----------------------------
;Try sierp1 2  5


to sierp1 :size :level
a :size :level
seth 90 fd :size
b :size :level
seth 180 fd :size
c :size :level
seth -90 fd :size
d :size :level
seth 0 fd :size
end

to a :size :level
if :level<1 [stop]
a :size :level-1
seth 90 fd :size
b :size :level-1
seth 0 fd :size rt 90 fd :size
d :size :level-1
seth 0 fd :size
a :size :level-1
end

to b :size :level
if :level<1 [stop]
b :size :level-1
seth 180 fd :size
c :size :level-1
seth 90 fd :size rt 90 fd :size
a :size :level-1
seth 90 fd :size
b :size :level-1
end

to c :size :level
if :level<1 [stop]
c :size :level-1
seth -90 fd :size
d :size :level-1
seth 180 fd :size rt 90 fd :size
b :size :level-1
seth 180 fd :size
c :size :level-1
end

to d :size :level
if :level<1 [stop]
d :size :level-1
seth 0 fd :size
a :size :level-1
seth -90 fd :size rt 90 fd :size
c :size :level-1
seth -90 fd :size
d :size :level-1
end


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   ---- File information -----------
     File:  map1.gif
     Date:  12 May 1998, 18:09
     Size:  3018 bytes.
     Type:  GIF-image

map1.gif