(This variant was requested by Mark Dominus.)
Associate Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
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This is still a XOR table, but now with the input sequence reordered so only one bit changes between each step. And since XOR preserves this property, also exactly one bit changes if you move horizontally or vertically in the table. And the input sequence can be calculated with XOR too: f(x) = x XOR (x SHR 1)
Not completely incidentally I used this sequence in my composition XOR! https://xor.glitch.me