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Seqfans,<br><br>
The following pattern of colors (which I hope you find pleasing) is based
on a Nim addition table<br>
for n = 0 to 31, m = 0 to 31. The color mapping starts with red = 0 then
goes around the spectrum<br>
as the value of the nimber increases, yellow = 5, green = 10, cyan = 15,
blue = 21, magenta = 26.<br>
See A003987 - Table of n XOR m (or Nim-sum of n and m) read by
antidiagonals, <br>
i.e. with entries in the order (n,m) =
(0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...<br>
<a href="http://www.research.att.com/~njas/sequences/A003987" eudora="autourl">http://www.research.att.com/~njas/sequences/A003987</a><br>
(I got turned onto nimbers from reading 'The Book of Numbers' by Conway
and Guy)<br><br>
<img src="cid:.0" width=652 height=586 alt="c9c2a3.jpg"><br><br>
To make the image I computed the values, put them into a web page that
uses css to map the colors,<br>
then used Paint Shop Pro to do a screen capture. Below are the values in
the addition table. If there's an interest<br>
I could put the web page on the internet. Images based on Nim
multiplication, powers etc. might be nice.<br><br>
<font face="Courier New, Courier" size=2> 0 1 2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26 27 28 29 30 31<br>
1 0 3 2 5 4 7 6
9 8 11 10 13 12 15 14 17 16 19 18 21 20 23 22 25 24 27 26 29 28 31
30<br>
2 3 0 1 6 7 4 5 10
11 8 9 14 15 12 13 18 19 16 17 22 23 20 21 26 27 24 25 30 31
28 29<br>
3 2 1 0 7 6 5 4 11
10 9 8 15 14 13 12 19 18 17 16 23 22 21 20 27 26 25 24 31 30
29 28<br>
4 5 6 7 0 1 2 3 12 13 14
15 8 9 10 11 20 21 22 23 16 17 18 19 28 29 30 31 24 25 26
27<br>
5 4 7 6 1 0 3 2 13 12 15
14 9 8 11 10 21 20 23 22 17 16 19 18 29 28 31 30 25 24 27
26<br>
6 7 4 5 2 3 0 1 14 15 12
13 10 11 8 9 22 23 20 21 18 19 16 17 30 31 28 29 26 27 24
25<br>
7 6 5 4 3 2 1 0 15 14 13
12 11 10 9 8 23 22 21 20 19 18 17 16 31 30 29 28 27 26 25
24<br>
8 9 10 11 12 13 14 15 0 1 2 3
4 5 6 7 24 25 26 27 28 29 30 31 16 17 18 19 20 21 22
23<br>
9 8 11 10 13 12 15 14 1 0 3 2
5 4 7 6 25 24 27 26 29 28 31 30 17 16 19 18 21 20 23
22<br>
10 11 8 9 14 15 12 13 2 3 0 1
6 7 4 5 26 27 24 25 30 31 28 29 18 19 16 17 22 23 20
21<br>
11 10 9 8 15 14 13 12 3 2 1 0
7 6 5 4 27 26 25 24 31 30 29 28 19 18 17 16 23 22 21
20<br>
12 13 14 15 8 9 10 11 4 5 6 7
0 1 2 3 28 29 30 31 24 25 26 27 20 21 22 23 16 17 18
19<br>
13 12 15 14 9 8 11 10 5 4 7 6
1 0 3 2 29 28 31 30 25 24 27 26 21 20 23 22 17 16 19
18<br>
14 15 12 13 10 11 8 9 6 7 4 5
2 3 0 1 30 31 28 29 26 27 24 25 22 23 20 21 18 19 16
17<br>
15 14 13 12 11 10 9 8 7 6 5 4
3 2 1 0 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17
16<br>
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 0 1
2 3 4 5 6 7 8 9 10 11 12 13 14
15<br>
17 16 19 18 21 20 23 22 25 24 27 26 29 28 31 30 1 0
3 2 5 4 7 6 9 8 11 10 13 12 15
14<br>
18 19 16 17 22 23 20 21 26 27 24 25 30 31 28 29 2 3
0 1 6 7 4 5 10 11 8 9 14 15 12
13<br>
19 18 17 16 23 22 21 20 27 26 25 24 31 30 29 28 3 2
1 0 7 6 5 4 11 10 9 8 15 14 13
12<br>
20 21 22 23 16 17 18 19 28 29 30 31 24 25 26 27 4 5
6 7 0 1 2 3 12 13 14 15 8 9 10
11<br>
21 20 23 22 17 16 19 18 29 28 31 30 25 24 27 26 5 4
7 6 1 0 3 2 13 12 15 14 9 8 11
10<br>
22 23 20 21 18 19 16 17 30 31 28 29 26 27 24 25 6 7
4 5 2 3 0 1 14 15 12 13 10 11 8
9<br>
23 22 21 20 19 18 17 16 31 30 29 28 27 26 25 24 7 6
5 4 3 2 1 0 15 14 13 12 11 10 9
8<br>
24 25 26 27 28 29 30 31 16 17 18 19 20 21 22 23 8 9 10 11 12
13 14 15 0 1 2 3 4 5 6
7<br>
25 24 27 26 29 28 31 30 17 16 19 18 21 20 23 22 9 8 11 10 13
12 15 14 1 0 3 2 5 4 7
6<br>
26 27 24 25 30 31 28 29 18 19 16 17 22 23 20 21 10 11 8 9 14
15 12 13 2 3 0 1 6 7 4
5<br>
27 26 25 24 31 30 29 28 19 18 17 16 23 22 21 20 11 10 9 8 15
14 13 12 3 2 1 0 7 6 5
4<br>
28 29 30 31 24 25 26 27 20 21 22 23 16 17 18 19 12 13 14 15 8
9 10 11 4 5 6 7 0 1 2
3<br>
29 28 31 30 25 24 27 26 21 20 23 22 17 16 19 18 13 12 15 14 9
8 11 10 5 4 7 6 1 0 3
2<br>
30 31 28 29 26 27 24 25 22 23 20 21 18 19 16 17 14 15 12 13 10 11
8 9 6 7 4 5 2 3 0
1<br>
31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10
9 8 7 6 5 4 3 2 1
0<br><br>
</font>Cheers,<br>
Gerald</body>
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