LOGO-L> fractals

[MHELHEFNY@FRCU.EUN.EG]

;Hello Keith Enevoldsen
;Members of logo-l surly had enjoied your successful single-liner contest.
;I am looking forward for another similar contest, which I suggest that you,
;if you have time can arrange it in the same manner as the first one.
;The new contest may not have size of code as the main limiting condition
;but the elegance of code, the beuty of resuls and complixty of drawings.
;this is achievrd with only one simple body procedure and a calling one.
;The subject of such new contest may be space filling curves, since as
;you know these curves may be fractals or non fractals.
;The space filling curves are those curves which arrise from an infinitly
;repeated construction process. strangely few regular fractals appeared
;outside Mandelbrot's book "fractal Geometry of Nature".
;Felix Hausdorff had set a dimension to fractals which is something in
;between the dimension of a line and that of an area i.e. a number more
;than one and less than two. By hausdorff's definition the dimension of
;the Koch's snow-flake fractal is 1.2618 while that of the Sierpinski
;carpet is 1.8928. While conventional dimension can only determine if
;an object does or does not fill a space, the Hausdorff dimension can 
;measure what fraction of the space an object covers (something like 
;measuring the density of a cloud). Fractals live in a nether world 
;between conventionally dimesioned spaces. 
;So koch's snowflake and Sierpinski's carpet live in a world between their 
;one-dimensional parts and their two-dimensional home. For example the 
;space which the Sierpinski carpet can cover on a square land will not 
;exeed 1.8928 of its area whatever was the number of repetiton levels. 
;The Hilbert curve which is the most famous of the space-filling curves 
;is not a fractal since its Hausdorff dimension is 2, more than any other 
;space filling curve.
;On the other hand a dragon is defined as an organism of cells arranged 
;according to a genetic code. It begins lifw as a single cell and then,
;by daily cell devision, grows into a creature with a shape and character
;governed by the "DNA" of its genetic code. This defintion includes both
;regular fractals and space filling curves. It is based on Dekking's
;notion of recurrent sets having its origins in Lindimayer's study of
;cell development and cellular automata. The most famous automaton
;is Conway's game of Life.
;Here are the names of the most famous space-filling curves:

;Hilbert curve          Koch's snow-flake      Heighway's dragon boundary
;Sierpinski's carpet    Gosper's curve         Heighway's dragon
;Heighway's interior    Heighways curd         Mandelbrot's arrow-head
;Brick curve            Pentigree curve        Lace curve
;Brick interior         Moor's necklace        Chrismas tree
;Mandelbrot's quintent  Dekking's church
   
;At the end of my message I hope will enjoy the shape of the following
;hexa_rose fractal. to diffrentiate between depth of levels I use pensize
;together with pencolor. the code runs on UCBlogo, for MSWlogo you can
;convert setpc  --> setpc [255 .. ..]

 
to hexa_rose :l :lev
if :lev=0 [stop]
repeat 6[setpc :lev+1 setpensize se :lev :lev 
repeat 30[fd :l rt 6] hexa_rose :l/2 :lev-1 rt 120]
end

to go
cs ht pu lt 17 setxy -68 -68 pd 
type [input depth 2- 5 ]type char 9 hexa_rose 5 rw
end

;Execuse me for this very long message thanks
;with best regards
;Mhelhefni
;Alazhar univ. Cairo Egypt
---------------------------------------------------------------
Please post messages to the Logo forum to logo-l@gsn.org.  Mail
questions about the list administration to logofdn@gsn.org.  To
unsubscribe send    unsubscribe logo-l    to majordomo@gsn.org.