(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 30115, 557] NotebookOptionsPosition[ 13666, 263] NotebookOutlinePosition[ 30201, 559] CellTagsIndexPosition[ 30158, 556] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`color$$ = True, $CellContext`extinput$$ = 0, $CellContext`init$$ = True, $CellContext`Iterations$$ = 20, $CellContext`LengthL$$ = 13, $CellContext`mesh$$ = True, $CellContext`rseed$$ = 1, $CellContext`rulenumber$$ = 170, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`LengthL$$], 8, "Length L"}, {3, 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ArrayPlot[$CellContext`CAwithinput = NestList[BitOr[ IntegerDigits[$CellContext`extinput$$, 2, $CellContext`LengthL$$], Flatten[ CellularAutomaton[$CellContext`rulenumber$$, #, 1, -1]]]& , BitOr[ IntegerDigits[$CellContext`extinput$$, 2, $CellContext`LengthL$$], Part[$CellContext`CAnoinput, 1]], $CellContext`Iterations$$], ImageSize -> {390, 390}, Frame -> None, Mesh -> $CellContext`mesh$$, ColorRules -> If[$CellContext`color$$, {0 -> Blue, 1 -> Red}, { 0 -> White, 1 -> Black}]]}, { If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 1], "Period 1", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 1], 1], "Bernoulli \[Tau]=1 \[Sigma]=1", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 1], -1], "Bernoulli \[Tau]=1 \[Sigma]=-1", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 2], 2], "Bernoulli \[Tau]=2 \[Sigma]=2", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 2], -2], "Bernoulli \[Tau]=2 \[Sigma]=-2", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 2], -1], "Bernoulli \[Tau]=2 \[Sigma]=-1", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 2], 1], "Bernoulli \[Tau]=2 \[Sigma]=1", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 2], "Period 2", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 3], "Period 3", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 4], "Period 4", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 6], "Period 6", If[ Part[$CellContext`CAnoinput, $CellContext`Iterations$$] == Part[$CellContext`CAnoinput, $CellContext`Iterations$$ - 12], "Period 12", "Other"]]]]]]]]]]]], If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 1], "Period 1", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 1], 1], "Bernoulli \[Tau]=1 \[Sigma]=1", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 1], -1], "Bernoulli \[Tau]=1 \[Sigma]=-1", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 2], 2], "Bernoulli \[Tau]=2 \[Sigma]=2", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 2], -2], "Bernoulli \[Tau]=2 \[Sigma]=-2", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 2], -1], "Bernoulli \[Tau]=2 \[Sigma]=-1", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == RotateLeft[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 2], 1], "Bernoulli \[Tau]=2 \[Sigma]=1", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 2], "Period 2", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 3], "Period 3", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 4], "Period 4", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 6], "Period 6", If[ Part[$CellContext`CAwithinput, $CellContext`Iterations$$] == Part[$CellContext`CAwithinput, $CellContext`Iterations$$ - 12], "Period 12", "Other"]]]]]]]]]]]]}}, Frame -> All]& )[ If[$CellContext`init$$, RandomInteger[1, $CellContext`LengthL$$], {{1}, 0}]]), "Specifications" :> {{{$CellContext`LengthL$$, 8, "Length L"}, {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100}}, {$CellContext`Iterations$$, 20, 100, 1, Appearance -> "Labeled"}, 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