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From: jbm@eos.UUCP (Jeffrey Mulligan)
Newsgroups: comp.windows.x,comp.graphics
Subject: Re: 4x4 Dithering Patterns?
Message-ID: <3797@eos.UUCP>
Date: 30 May 89 19:40:57 GMT
References: <31971@bu-cs.BU.EDU>
Organization: NASA Ames Research Center, California
Lines: 61

From article <31971@bu-cs.BU.EDU>, by bzs@bu-cs.BU.EDU (Barry Shein):
 
> Is there more order than I describe here? Perhaps I should have gone
> to the library first and sorted through papers

You said it, not me

> but perhaps someone on
> this list will point me towards some and save me some time.
> -- 
> 	-Barry Shein

Algorithms for generating the arrays are described in Ulichney's
recent book (Digital Halftoning) which is often cited on this newsgroup.
The seminal reference seems to be

	Bayer, B.E. (1973)  "An optimum method for two level rendition
	of continuous tone pictures", Proc. IEEE Int. Conf. Commun.
	Conference Record, pp. (26-11)-(26-15).

A simple way to do this without going to the library is to start with
a small pattern:

	0 2
	3 1

And double it in size by multiplying the original by four, repicating,
and adding the elements of the original to each block:

	times 4	            0  8
			    12 4

	replicate           0  8 0  8
			    12 4 12 4
			    0  8 0  8
			    12 4 12 4

			       +

			    0 0 2 2
			    0 0 2 2
			    3 3 1 1
			    3 3 1 1

			       =

			    0  8  2  10
			    12 4  14 6
			    3  11 1  9
			    15 7  13 5


Gee, I meant to leave some of the work for you.

Happy dithering.

-- 

	Jeff Mulligan (jbm@aurora.arc.nasa.gov)
	NASA/Ames Research Ctr., Mail Stop 239-3, Moffet Field CA, 94035
	(415) 694-6290