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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. …
Halbort's user avatar
  • 1,129
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. …
Halbort's user avatar
  • 1,129
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. …
Halbort's user avatar
  • 1,129
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. …
Halbort's user avatar
  • 1,129