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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.

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• Groups

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