From: Morton Goldberg <m_goldberg@...>
Date: 2007-05-26T08:53:16+09:00
Subject: Re: [QUIZ] Fractals (#125)

On May 25, 2007, at 9:18 AM, Ruby Quiz wrote:

> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- 
> =-=-=-=-=-=-=
>
> by Drew Olson
>
> When I learned about fractals in high school math class, I  
> immediately found
> them fascinating. For those of you unfamiliar with the concept, the  
> definition
> from Wikipedia is as follows: a fractal is "a rough or fragmented  
> geometric
> shape that can be subdivided in parts, each of which is (at least  
> approximately)
> a reduced-size copy of the whole".
>
> At the end of the unit in which we were taught them, the fractal  
> below was a
> test question. In subsequent years, I began drawing it freehand to  
> higher and
> higher levels. The details and patterns that emerge are fascinating.
>
> The goal is to create a ruby program which takes the level as an  
> argument and
> then draws the fractal shown below to the specified level. The  
> fractal is
> created by drawing the first level, then repeating the pattern such  
> that each
> base piece is replaced with the fractal from the higher level.  
> Thus, to move
> from level 1 to level 2, we replace each line with the shape at  
> level 1. Notice
> that the position changes as well, meaning if the line is vertical  
> we replace it
> with a vertically positioned shape of level 1 (right and left  
> facing also
> matter). I have shown the first 3 levels below (including the base  
> component at
> level 0). Feel free to use the console for output or get fancy with  
> RMagick or
> something similar.
>
> 	                          _                  <-- Level 0
> 	                          _
> 	                        _| |_                <-- Level 1
> 	                          _
> 	                        _| |_
> 	                      _|     |_              <-- Level 2
> 	                    _|_       _|_
> 	                  _| |_|     |_| |_
> 	
> 	                          _
> 	                        _| |_
> 	                      _|     |_
> 	                    _|_       _|_
> 	                  _| |_|     |_| |_
> 	                _|                 |_
> 	              _|_                   _|_
> 	            _| |_|                 |_| |_    <-- Level 3
> 	          _|                             |_
> 	        _|_                               _|_
> 	      _| |_|_   _                   _   _|_| |_
> 	    _|     |_|_|_|                 |_|_|_|     |_
> 	  _|_       _|_|_                   _|_|_       _|_
> 	_| |_|     |_| |_|                 |_| |_|     |_| |_
>

I'm confused about the intent of this quiz. Is the main focus writing  
code that will re-create the ASCII art shown above, or is it just to  
draw the required fractal by any means of the solver's choice (for  
example, using the turtle geometry classes developed in Quiz 104)? If  
the latter is permitted, a simple, recursive turtle program will do  
the job.

Regards, Morton