Difference between revisions of "Notes:Grid iteration"
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See [[Modulo operator]] for a definition of {{M|\text{Mod}(a,b)}} | See [[Modulo operator]] for a definition of {{M|\text{Mod}(a,b)}} | ||
==2D grid== | ==2D grid== | ||
| + | [[File:2dGridReproduction small 4by5.gif|thumbnail|Notice the 21st point is back at the origin and the sequence repeats. [https://wiki.unifiedmathematics.com/index.php?title=File:2dGridReproduction_small_4by5.gif Direct link]]] | ||
* {{MM|\text{Mix}_x(k,m,n):\eq \text{Floor}\left(\text{Mod}\big(\text{Mod}(k,mn),m\big)\right)}} | * {{MM|\text{Mix}_x(k,m,n):\eq \text{Floor}\left(\text{Mod}\big(\text{Mod}(k,mn),m\big)\right)}} | ||
* {{MM|\text{Mix}_y(k,m,n):\eq \frac{\text{Mod}(k,mn)-\text{Mod}\big(\text{Mod}(k,mn),m\big)}{m} }} | * {{MM|\text{Mix}_y(k,m,n):\eq \frac{\text{Mod}(k,mn)-\text{Mod}\big(\text{Mod}(k,mn),m\big)}{m} }} | ||
Revision as of 18:28, 7 January 2018
See Modulo operator for a definition of [ilmath]\text{Mod}(a,b)[/ilmath]
2D grid
Notice the 21st point is back at the origin and the sequence repeats. Direct link
- [math]\text{Mix}_x(k,m,n):\eq \text{Floor}\left(\text{Mod}\big(\text{Mod}(k,mn),m\big)\right)[/math]
- [math]\text{Mix}_y(k,m,n):\eq \frac{\text{Mod}(k,mn)-\text{Mod}\big(\text{Mod}(k,mn),m\big)}{m} [/math]
Then
- Points of the form:
- [math]\big(\text{Mix}_x(k,m,n),\text{Mix}_y(k,m,n)\big)[/math] span an [ilmath]m\times n[/ilmath] grid, for [ilmath]k[/ilmath] from [ilmath]0[/ilmath] to [ilmath]mn-1[/ilmath]
3D grid
Suppose we have an [ilmath]\ell\times m\times n[/ilmath] grid,
