I haven't has a chance to read the Advance Aquarist article yet but will as soon as I can.  Here is what I understand to be the current thinking on LED spacing with various optics to get good blending: 
 
40 degree - 1.5"-2" 
60 degree - 2"-2.5" 
80 degree - 2.5"-3.5" 
 
With no optics you could probably go 4 or 5 inches apart but won't get much PAR deeper in the tank.  Spacing of rows front to back can be a bit wider as the spotlighting effect will not be as noticeable.  So maybe 3 to 4 inches between rows.  Personally I would only go no optics on a nano or shallow tank (12 inches or less).  I am using 60 degree optics for mine (20" deep) and have spaced the LEDs 2.25 inches apart and the rows are 3 inches apart front to back. 
 
I should also add that I have alternated the white and blue in the row rather than go with separate rows of white and blue like the one in the pictures. 
		
	
		
		
		
		
		
	
		
		
	
	
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