Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site kovacs.UUCP
Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!ittvax!dcdwest!sdcsvax!sdcrdcf!randvax!kovacs!rivero
From: rivero@kovacs.UUCP (Michael Foster Rivero)
Newsgroups: net.graphics
Subject: fractal mountains
Message-ID: <241@kovacs.UUCP>
Date: Tue, 18-Jun-85 19:58:15 EDT
Article-I.D.: kovacs.241
Posted: Tue Jun 18 19:58:15 1985
Date-Received: Mon, 24-Jun-85 03:42:22 EDT
Organization: Robt Abel & Assoc, Hollywood
Lines: 105
Keywords: fractals

---------------------------------------


	In regards  to  Rich  Stewart's  excerpted  paper  on  fractal
	subdivision.


>       1) Choose a triangle
>
>       2) Choose a point, with a high probability of being
>          inside the current triangle.
>
>       3)  Create a new triangle by connecting the  new  point
>       to the vertices of side A.
>
>       4) Recurse on this new triangle to make new smaller
>          triangles on it.
>
>       5) Choose a point, with a high probability of being
>          inside the current triangle.
>
>       6)  Create a new triangle by connecting the new point
>          to the vertices of side B.
>
>       7) Recurse on this new triangle to make new smaller
>          triangles on it.
>
>       8) Choose a point, with a high probability of being
>          inside the current triangle.
>
>       9)  Create a new triangle by connecting the  new  point
>       to the vertices of side C.
>
>       10) Recurse on this new triangle to make new smaller
>           triangles on it.
>
>


	  Close examination of the above will reveal that all three of
	the  smaller  triangles  share  a  common side with the larger
	triangles. A simple diagram would be....


			       /|\
			      / | \
			     /  |  \
			    /   |   \
			   /    |    \
			  /     |     \
			 /    ,' ',    \
			/   ,'     ',   \
		       /  ,'         ',  \
		      / ,'             ' ,\
		     /,'__________________'\



	  Its main drawback is that even at the limits  of  recursion,
	there  will  always  be triangles with one of the vertecies of
	the starting figure, albeit very long and very thin. This will
	produce images with long thin triangular artifacts.





	  A better approach, (and the one I use) displaces the center of
	each vertex by a random amount. The new triangles are built from
	one existing vertex, and two displaced centerpoints, thus....

			       /\
			      /  \
			     /    \
			    /      \
			   /________\
			  /\        /\
			 /  \      /  \
			/    \    /    \
		       /      \  /      \
		      /________\/________\

	  As you can see, each triangle retains a  fairly  equalateral
	shape, and decreases in size in direct proportion to the level
	of recursion.  By seeding the  random  displacement  generator
	with  a combination of all 6 end verticies, sides of adjoining
	triangles  will  produce  identical  midpoint   displacements,
	eliminating  "holes"  in  the final fractal form.  This allows
	one to apply a psuedo-fractal surface to a predefined form.

	  Sorry Rich! You're busted!


					Michael Rivero






     On a note of  personal  interest.  I cut my graphics teeth
with NASA. I already make a living off of drawing pretty pic-
tures on computers.

( Lucas films, I will see you at SIGGRAPH!!!)