The Multi-circulate Method
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The multi-circulate method “กก ” !ก" “กก ” กก#$!ก! !!" 2 %& !' +1
-1
+1
+1
ก#$! $ ก! X !( " ก#$! $ ก! X ! "ก ก#$! $ ก! Y !"! "ก ก#$! $ ก! Y ! "
กก 1.
% !ก#$! )$ ( %*+!' ก “Cell” +ก" %& 2 %& %& ก ) %#$! ก! X %& ) ) %#$! ก! Y Cell !, ) ! !+ Cell(0,0)
กก %&% ก! - $ "ก $ " 1 % ก!!&'!- & %& , 2.
2.
กก % ! ก Cell(0,0) ก %&*+ &' 4 ! ก %&*+ !"! +.! Cell(0,1) ก %&*+ ! +.! Cell(1,0) ก %&*+ ! +.! Cell(0,-1) ก %&*+ !( +.! Cell(-1,0) ) !+.!/!,* & !' 00
01
10
0-1
-10
กก Cell $ Cell $ !&'! ) ก %&* ก 4 0"%& !
Cell (0,1) ) ก %&* ก 4 0 !"!, ! , ! , !( Cell (1,0) ) ก %&* ก 4 0 !"!, ! , ! , !( Cell (0,-1) ) ก %&* ก 4 0 !"!, ! , ! , !( Cell (-1,0) ) ก %&* ก 4 0 !"!, ! , ! , !(
3.
กก %& ก '! ก Cell(0,1) ก Cell $ - Cell(0,2) !"! - Cell(1,1) ! - Cell(0,0) ! - Cell(-1,1) !( Cell(1,0) ก Cell $ - Cell(1,1) !"! - Cell(2,0) ! - Cell(1,-1) ! - Cell(0,0) !( Cell(0,-1) ก Cell $ - Cell(0,0) !"! - Cell(1,-1) ! - Cell(0,-2) ! - Cell(-1,-1) !( Cell(-1,0) ก Cell $ - Cell(-1,1) !"! - Cell(0,0) ! - Cell(-1,-1) ! - Cell(-2,0) !(
) !+.!/!,* & !'
ก#$! n #!!&' !กก %& #!! Cell &' $ !กก %& n &' *
= 4 +
= 1
#!! Cell $ ก '! !กก %& n &' +.! Cell * ('#ก&"%#$! ก&! ก “Cell ” = #!! Cell !กก %& n &' * = 2 + 2 + 1
กกก %& ก Cell %#$! ก&! ก “Cell ('#ก&!” #!! Cell ('#ก&! & ' $
กก %& n &'
ก )& &!1
#!! Cell &' $ !กก %& n &' = #!! Cell + #!! Cell ('#ก&! ∴ #!! Cell ('#ก&! = #!! Cell &' $ !กก %& - #!! Cell = -
$
= – 2 - 2 - 1
-1
+1
+1
ก#$! $ ก! X !( " ก#$! $ ก! X ! "ก ก#$! $ ก! Y !"! "ก ก#$! $ ก! Y ! "
กก 1.
% !ก#$! )$ ( %*+!' ก “Cell” +ก" %& 2 %& %& ก ) %#$! ก! X %& ) ) %#$! ก! Y Cell !, ) ! !+ Cell(0,0)
กก %&% ก! - $ "ก $ " 1 % ก!!&'!- & %& , 2.
2.
กก % ! ก Cell(0,0) ก %&*+ &' 4 ! ก %&*+ !"! +.! Cell(0,1) ก %&*+ ! +.! Cell(1,0) ก %&*+ ! +.! Cell(0,-1) ก %&*+ !( +.! Cell(-1,0) ) !+.!/!,* & !' 00
01
10
0-1
-10
กก Cell $ Cell $ !&'! ) ก %&* ก 4 0"%& !
Cell (0,1) ) ก %&* ก 4 0 !"!, ! , ! , !( Cell (1,0) ) ก %&* ก 4 0 !"!, ! , ! , !( Cell (0,-1) ) ก %&* ก 4 0 !"!, ! , ! , !( Cell (-1,0) ) ก %&* ก 4 0 !"!, ! , ! , !(
3.
กก %& ก '! ก Cell(0,1) ก Cell $ - Cell(0,2) !"! - Cell(1,1) ! - Cell(0,0) ! - Cell(-1,1) !( Cell(1,0) ก Cell $ - Cell(1,1) !"! - Cell(2,0) ! - Cell(1,-1) ! - Cell(0,0) !( Cell(0,-1) ก Cell $ - Cell(0,0) !"! - Cell(1,-1) ! - Cell(0,-2) ! - Cell(-1,-1) !( Cell(-1,0) ก Cell $ - Cell(-1,1) !"! - Cell(0,0) ! - Cell(-1,-1) ! - Cell(-2,0) !(
) !+.!/!,* & !'
ก#$! n #!!&' !กก %& #!! Cell &' $ !กก %& n &' *
= 4 +
= 1
#!! Cell $ ก '! !กก %& n &' +.! Cell * ('#ก&"%#$! ก&! ก “Cell ” = #!! Cell !กก %& n &' * = 2 + 2 + 1
กกก %& ก Cell %#$! ก&! ก “Cell ('#ก&!” #!! Cell ('#ก&! & ' $
กก %& n &'
ก )& &!1
#!! Cell &' $ !กก %& n &' = #!! Cell + #!! Cell ('#ก&! ∴ #!! Cell ('#ก&! = #!! Cell &' $ !กก %& - #!! Cell = -
$
= – 2 - 2 - 1
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