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Colour Octonions
I was idly trying to create some groups for fun. I remembered from a while ago when someone asked me "Can you do maths with colours?" I have now figured that you can. I used the RGB scale and the Ex-Or combining operation. This will soon be explained.
There are 8 colours. These are Black, Red, Green, Blue, Cyan, Magenta, Yellow, and White. Each colour also has a 3-bit ID. The first bit is whether it has red, the second green, and the third blue. Here is a table.
| Colour |
ID |
Octonion |
| Black |
000 |
1 |
| Cyan |
011 |
i |
| Magenta |
101 |
j |
| Yellow |
110 |
k |
| White |
111 |
l |
| Red |
100 |
m |
| Green |
010 |
n |
| Blue |
001 |
o |
To combine colours, take the exclusive-or of each bit. Now what does this
have to do with octonions? Let black be 1 and the other colours be the letters
e.g. i, j, k, l, m, n, and o. The combining operation is plus or minus their
product in octonions. This makes it fairly simple to memorise which octonion
results. However, the sign must still be learned.
Related entries
• Groups
• Complex Matters
• Octonions
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