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1
vote
Nim and the Sierpinski Gasket
Although the connection between Nim and the Sierpinski Gasket has not been explicitly proven (or I have not seen it), I would hesitate to believe that no one has thought of it before. … The reason being the obvious connection Nim and the bitwise xor.
It turns out that the bitwise xor is intricately connected with Sierpinski Gasket. …
5
votes
0
answers
304
views
Generalization of Sprague-Grundy Theorem
This theorem is just Sprague-Grundy using Moore's Nim rather than normal Nim. So how should I cite this? … As I said previously, I am hesitant to claim the result because it relies so heavily on Moore's Nim. On the other hand, I have not found it anywhere. …
3
votes
0
answers
700
views
Nimbers and Surreal Numbers [closed]
Nimbers essentially relate a position in a normal impartial game to a nim heap.
My question is that can the nimbers be interpreted in the concept of surreal numbers. …
15
votes
3
answers
2k
views
Why does the bitxor function appear in Nim?
Although I have done a considerable amount of reading, I do not completely understand why the bit-xor function also known as the nim-sum appears in Nim. … I was reading A paper of Fraenkel and Kontorovich which used the bitwise and to explore Nim. …