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What is the Hilbert curve's equation?! In the question linked, there is a formula for Hilbert Curve. It involves $e_{kj}$ and $d_j$ terms. It says that $e_{kj}$ denotes number of k's preceding $q_j$ and $d_j \equiv e_{0j} + e_{3j} \text{ (mod 2)}$.

Can someone clearly explain how to find $e_{kj}$? And to find $d_j$ do you take modulo of the sum or modulo of $e_3j$?

Lê Thành Đạt
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Aleksander
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  • Do you understand what is meant by the base $4$ expansion of $t$? $e_{kj}$ is the number of $k$'s in the first $j-1$ base $4$ expansion of $t$. $k$ must be one of $0,1,2,3$ for this to make sense. – saulspatz Jun 05 '19 at 16:13
  • @saulspatz I do understand base four expansion. So, from what you said for a number $0.0122333$, $e_{07} = 1$ and $e_{37} = 2$, right? Also, could you clarify for me: is $d_j$ equal to $e_{0j} + (e_{3j} mod2)$ or $(e_{0j} + e_{3j}) mod2$? – Aleksander Jun 05 '19 at 17:46
  • Yes, that's how I understand it. It means $(e_{0j} + e_{3j}) \pmod{2}$ – saulspatz Jun 05 '19 at 17:59

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