Hi Rachel,

A quick hint :)

The function that's responsible for drawing a single star should take
the *center* of the star as its arguments.  Repeat, *center*, not top.

(Just to make sure I wasn't fibbing, I actually wrote the program
myself and just for the heck of it, I'll send the images generated by
the star program...)

Randy


>  From: "Rachel Gottron" <rgottron@princeton.edu> 
>  To: <rywang@CS.Princeton.EDU> 
>  Subject: recursive program 
>  Date: Fri, 27 Feb 2004 00:42:25 -0500 
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>   
>  Hi, 
>   
>  I actually got the HTree.java program to work, and now I'm working on my 
>  own Art.java program.  I'm trying to do the 5-point star fractal 
>  pattern, where at each vertex of the star a new star is drawn.  I've 
>  been working on this for HOURS, and I can't figure out what to do.  I've 
>  drawn the original star in 2 ways:  one by  
>   
>  		Turtle.fly(x,y) 
>  		Turtle.rotate(-72); 
>  		Turtle.goForward(size); 
>  		Turtle.rotate(-144); 
>  		Turtle.goForward(size); 
>  		Turtle.rotate(-144); 
>  		Turtle.goForward(size); 
>  		Turtle.rotate(-144); 
>  		Turtle.goForward(size); 
>  		Turtle.rotate(-144); 
>  		Turtle.goForward(size); 
>   
>  And the other one by: 
>   
>  		Turtle.fly(x, y); 
>  		x = x + size*(Math.cos(72*3.14/180));  
>  		y = y - size*(Math.sin(72*3.14/180)); 
>  		Turtle.go(x, y); 
>  		x = x - size*Math.sin(54*3.14/180);  
>  		y = y + size*Math.cos(54*3.14/180); 
>  		Turtle.go(x, y); 
>  		x = x + size;  
>  		Turtle.go(x, y); 
>  		x = x - size*Math.sin(54*3.14/180);  
>  		y = y - size*Math.cos(54*3.14/180); 
>  		Turtle.go(x, y); 
>  		x = x + size*Math.sin(18*3.14/180);  
>  		y = y + size*Math.cos(18*3.14/180); 
>  		Turtle.go(x, y); 
>   
>  Both of these programs lead to drawing the original star.  However, I 
>  don't know how to do this recursively.  The locations of the star 
>  vertices are much more complicated than the HTree.  Is there a way to 
>  change the axes?  If I try to write a recursive program to draw the 
>  stars, I have no way to refer to the vertices.  The only way I can think 
>  of to do this is to draw one segment of the star, then rotate and draw 
>  the first segment of a new, smaller star, then rotate and draw the first 
>  segment of a new and still smaller star, until I've arrived at the 
>  correct depth, at which point I start completing the stars. 
>  Unfortunately, it seems like this program will be very complicated and 
>  it could be tail-recursive.  I'm giving up for tonight, cause I don't 
>  know what else to do.  Let me know if I can explain this better.  I'll 
>  be in precept tomorrow and I'll probably stay for office hours (but I'm 
>  worried that there will be a lot of people there).  Thanks for your 
>  time! 
>   
>  ~Rachel 
>