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From: bayes@hpfcrj.UUCP
Newsgroups: comp.graphics
Subject: wanted: 16x16 or larger dither matrix
Message-ID: <3960001@hpfcrj.HP.COM>
Date: Fri, 6-Feb-87 14:23:30 EST
Article-I.D.: hpfcrj.3960001
Posted: Fri Feb  6 14:23:30 1987
Date-Received: Mon, 9-Feb-87 02:29:32 EST
References: <17010@ucbvax.BERKELEY.EDU>
Organization: HP Ft. Collins
Lines: 48

Re generating 16x16 dither matrix from 8x8:

One method is to replicate the 8x8 4 times into a 16x16 array, after
multiplying the original by 4. Viz:

	+---+---+
	|x4 |x4 |
	+---+---+
	|x4 |x4 |
	+---+---+

Now add 0 to each value in the upper left quadrant, 1 to each in lower right,
3 to each in upper right, and 2 to each in lower left. You can swap the 
values to add diagonally, but not along a row or column.

An example of expanding 2x2 to 4x4 follows.

The original:

	0    3

	2    1

Replicate, multiplying by 4:

	0   12     0  12
	8    4     8   4

	0   12     0  12
	8    4     8   4

Add:

	0   12     3  15
	8    4    11   7

	2   14     1  13
	10   6     9   5

This process is completely recursive, and you can start at a 1x1 dither
matrix [0], and work up to any 2^n x 2^n. I don't know a non-recursive
formula for any n, but am sure it's not hard to figure out.

Scott Bayes
hpfcla!bayes

This algorithm was independently arrived at by me, and I am not
representing Hewlett-Packard or any company in this note.