Dynamic Numbering | ||||
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The following formalises "Dynamic Numbering" | ||||
Generating Squares |
Generating squares can be formulated as products of "Normal Rectangles" which allows the formula |
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(_{i=0}∏^{n} _{pi}N_{qi})[x,y] =
_{i=0}∑^{n} _{k=0}∏^{i} p_{k}q_{k} { ([x % _{k=0}∏^{i} p_{k}] \ _{k=0}∏^{i-1} p_{k}) + p_{n} ([y % _{k=0}∏^{i} q_{k}] \ _{k=0}∏^{i-1} q_{k}) }; _{i=0}∏^{n} p_{i} = _{i=0}∏^{n} q_{i} = m |
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Examples up till 4 rectangles: (_{p}N_{q} * _{r}N_{s})[x,y] = (x%r) + r (y%s) + rs [(x\r) + p (y\s)] (_{t}N_{u} * _{p}N_{q} * _{r}N_{s})[x,y] = (x%r) + r (y%s) + rs [((x%pr)\r) + p ((y%qs)\s)] + pqrs [(x\pr) + t (y\qs)] (_{v}N_{w} * _{t}N_{u} * _{p}N_{q} * _{r}N_{s})[x,y] = (x%r) + r (y%s) + rs [((x%pr)\r) + p ((y%qs)\s)] + pqrs [((x%prt)\pr) + t ((y%qsu)\qs)] + pqrstu [(x\prt + v (y\qsu)] |
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Coordinate Squares |
A coordinate square is a (magic) square in analitic numberrange where the numbers are transformed into coordinates |
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MS[x,y] => [ MS[x,y] % m, MS[x,y] \ m ]. | ||||
Generated Squares | Using the coordinate Square into the Generating Square Generates a new square | |||
S[x,y] => GS[ MS[x,y] % m, MS[x,y] \ m ]. |