Notes:Grid iteration

See Modulus operator for a definition of $\text{Mod}(a,b)$

2D grid

• $$\text{Mix}_x(k,m,n):\eq \text{Floor}\left(\text{Mod}\big(\text{Mod}(k,mn),m\big)\right)$$
• $$\text{Mix}_y(k,m,n):\eq \frac{\text{Mod}(k,mn)-\text{Mod}\big(\text{Mod}(k,mn),m\big)}{m}$$

Then

• Points of the form:
  • $$\big(\text{Mix}_x(k,m,n),\text{Mix}_y(k,m,n)\big)$$ span an $m\times n$ grid, for $k$ from $0$ to $mn-1$

3D grid

Suppose we have an $\ell\times m\times n$ grid,