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Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]} + }, + AutoDelete->False, + GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], + "Grid"]], "Output", + CellChangeTimes->{{3.920279978489007*^9, 3.9202800059090514`*^9}, + 3.920281166469138*^9}, + TextAlignment->Center, + CellLabel->"3/24/24 16:59:26 Out[16]=", + CellID->397291535,ExpressionUUID->"dfd01e67-d611-4c3e-aa0e-2487522ca13a"] +}, Open ]] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Caption", + Cell[BoxData[ + TemplateBox[{"Caption", + Cell[ + BoxData[ + FrameBox[ + Cell[ + TextData[{ + "The caption provides all the information needed to understand the \ +Demonstration. It should be between three and five sentences long, but \ +clarity is more important than length. Include only text in this section \ +\[LongDash] no code, graphics, etc. Do not change the cell style or copy \ +cells from other sections. Do not copy text from books or the web. Write your \ +ideas in your own words. If you want to refer to something on the web, link \ +to it in the Details.", + StyleBox["\n", FontSize -> 4]}], "MoreInfoText"], Background -> + GrayLevel[0.95], FrameMargins -> 20, FrameStyle -> GrayLevel[0.9], + RoundingRadius -> 5]], "MoreInfoText", Deletable -> True, + CellTags -> {"SectionMoreInfoDefinition"}, + CellMargins -> {{66, 66}, {15, 15}}]}, + "MoreInfoOpenerButtonTemplate"]],ExpressionUUID-> + "a97b5d36-1c59-4018-b3f0-6bfc71662d3d"] +}], "ManipulateCaptionSection", + TextAlignment->Center, + CellTags->"Caption",ExpressionUUID->"3ed78bfd-4459-4d2a-906f-3e9e6aba33a4"], + +Cell["", "ManipulateCaption", + CellChangeTimes->{{3.9202807668171234`*^9, 3.9202807687471256`*^9}}, + TextAlignment->Center,ExpressionUUID->"71921e4e-c8c2-4f05-96e3-4e3047349e9a"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Thumbnail", + Cell[BoxData[ + TemplateBox[{"Thumbnail", + Cell[ + BoxData[ + FrameBox[ + Cell[ + TextData[{ + "To create the thumbnail, copy and paste the output cell from the ", + StyleBox["Manipulate", "MRbig"], + " section and adjust the controls to the most visually appealing \ +setting. Do not convert it to a bitmap. The thumbnail is what visitors see \ +when browsing the Demonstrations site and while the Flash preview loads.", + StyleBox["\n", FontSize -> 4]}], "MoreInfoText"], Background -> + GrayLevel[0.95], FrameMargins -> 20, FrameStyle -> GrayLevel[0.9], + RoundingRadius -> 5]], "MoreInfoText", Deletable -> True, + CellTags -> {"SectionMoreInfoDefinition"}, + CellMargins -> {{66, 66}, {15, 15}}]}, + "MoreInfoOpenerButtonTemplate"]],ExpressionUUID-> + "5363174b-397a-4e31-b8e5-95e1af887bc9"] +}], "ThumbnailSection", + TextAlignment->Center, + CellTags->"Thumbnail",ExpressionUUID->"401cc3c4-8319-4e19-82e7-df5fcb711a42"], + +Cell[BoxData[ + TagBox[GridBox[{ + { + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`\:1450\:1455$$ = 4, $CellContext`M$$ = + 0, $CellContext`\[CapitalPi]$$ = + 2, $CellContext`\[CapitalPi]\[CapitalPi]$$ = 16, Typeset`show$$ = + True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`\[CapitalPi]$$], 2}, 0, 16, 0.25}, {{ + Hold[$CellContext`\:1450\:1455$$], 4}, 0, 16, 0.25}, {{ + Hold[$CellContext`M$$], 0}, 0, 1, 0.125}, {{ + Hold[$CellContext`\[CapitalPi]\[CapitalPi]$$], 8}, 0, 16, 1}}, + Typeset`size$$ = {320., {222., 229.}}, Typeset`update$$ = 0, + Typeset`initDone$$, Typeset`skipInitDone$$ = True}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, + "Variables" :> {$CellContext`\:1450\:1455$$ = 4, $CellContext`M$$ = + 0, $CellContext`\[CapitalPi]$$ = + 2, $CellContext`\[CapitalPi]\[CapitalPi]$$ = 8}, + "ControllerVariables" :> {}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, + Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Column[{ + $CellContext`CurvaturePlot[ + Evaluate[ + SetPrecision[ + + SetAccuracy[(1 - + Abs[((-1)^ + Floor[(($CellContext`x/Pi) $CellContext`\:1450\:1455$$ + + 1)/2] Abs[ + 1 - Abs[ + Mod[($CellContext`x/Pi) $CellContext`\:1450\:1455$$ + 1, + 2] - 1]^$CellContext`\[CapitalPi]$$]^( + 1/$CellContext`\[CapitalPi]$$))/2 + + 0.5]) - $CellContext`M$$, Infinity], + Infinity]], {$CellContext`x, 0, 4 Pi}, + Evaluate[$CellContext`\:1513\:1515], FrameTicks -> { + Range[-16, 16, 1/2], + Range[-4, 4, 1/2]}, PlotPoints -> + 1 + 2^$CellContext`\[CapitalPi]\[CapitalPi]$$], + Plot[ + Evaluate[ + SetPrecision[ + SetAccuracy[ + 0.5 - (1 - + Abs[((-1)^ + Floor[(($CellContext`x/Pi) $CellContext`\:1450\:1455$$ + + 1)/2] Abs[ + 1 - Abs[ + Mod[($CellContext`x/Pi) $CellContext`\:1450\:1455$$ + 1, + 2] - 1]^$CellContext`\[CapitalPi]$$]^( + 1/$CellContext`\[CapitalPi]$$))/2 + + 0.5]) - $CellContext`M$$, Infinity], + Infinity]], {$CellContext`x, 0, 4 Pi}, + Evaluate[$CellContext`\:1513\:1515], AspectRatio -> 1/8, + FrameTicks -> { + Range[(-16) Pi, 16 Pi, Pi/2], + Range[-1, 1, 1/2]}, PlotPoints -> + 1 + 2^$CellContext`\[CapitalPi]\[CapitalPi]$$]}], + "Specifications" :> {{{$CellContext`\[CapitalPi]$$, 2}, 0, 16, + 0.25}, {{$CellContext`\:1450\:1455$$, 4}, 0, 16, + 0.25}, {{$CellContext`M$$, 0}, 0, 1, + 0.125}, {{$CellContext`\[CapitalPi]\[CapitalPi]$$, 8}, 0, 16, + 1}}, "Options" :> {FrameMargins -> 0}, + "DefaultOptions" :> {ControllerLinking -> True}], + ImageSizeCache->{345., {334., 341.}}, + SingleEvaluation->True], + Deinitialization:>None, + DynamicModuleValues:>{}, + SynchronousInitialization->True, + UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$}, + UnsavedVariables:>{Typeset`initDone$$}, + UntrackedVariables:>{Typeset`size$$}], "Manipulate", + Deployed->True, + StripOnInput->False], + Manipulate`InterpretManipulate[1]]} + }, + AutoDelete->False, + GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], + "Grid"]], "Output", + CellChangeTimes->{{3.920279978489007*^9, 3.9202800059090514`*^9}}, + TextAlignment->Center, + CellID->63458145,ExpressionUUID->"1b37c0f7-f862-4bde-95eb-3c9910bdd789"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[TextData[{ + "Snapshots", + Cell[BoxData[ + TemplateBox[{"Snapshots", + Cell[ + BoxData[ + FrameBox[ + Cell[ + TextData[{"To create snapshots, paste the output cell from the ", + StyleBox["Manipulate", "MRbig"], + " section in this section at least three times, and adjust the \ +controls of each copy to show a range of interesting settings. Do not convert \ +the screenshots to bitmaps. Optional captions for the screenshots may be \ +included in the Details section.", + StyleBox["\n", FontSize -> 4]}], "MoreInfoText"], Background -> + GrayLevel[0.95], FrameMargins -> 20, FrameStyle -> GrayLevel[0.9], + RoundingRadius -> 5]], "MoreInfoText", Deletable -> True, + CellTags -> {"SectionMoreInfoDefinition"}, + CellMargins -> {{66, 66}, {15, 15}}]}, + "MoreInfoOpenerButtonTemplate"]],ExpressionUUID-> + "d854de0f-efbb-449a-8b04-a7b3ca5773d5"] +}], "SnapshotsSection", + TextAlignment->Center, + CellTags->"Snapshots",ExpressionUUID->"96bb7a68-4496-4362-86d3-c2a0812907f2"], + +Cell[BoxData[ + RowBox[{ + TagBox[GridBox[{ + { + TagBox[ + StyleBox[ + DynamicModuleBox[{$CellContext`\:1450\:1455$$ = 4, $CellContext`M$$ = + 0, $CellContext`\[CapitalPi]$$ = + 0.5, $CellContext`\[CapitalPi]\[CapitalPi]$$ = 16, Typeset`show$$ = + True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", + Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = + "\"untitled\"", Typeset`specs$$ = {{{ + Hold[$CellContext`\[CapitalPi]$$], 2}, 0, 16, 0.25}, {{ + Hold[$CellContext`\:1450\:1455$$], 4}, 0, 16, 0.25}, {{ + Hold[$CellContext`M$$], 0}, 0, 1, 0.125}, {{ + Hold[$CellContext`\[CapitalPi]\[CapitalPi]$$], 8}, 0, 16, 1}}, + Typeset`size$$ = {320., {222., 229.}}, Typeset`update$$ = 0, + Typeset`initDone$$, Typeset`skipInitDone$$ = True}, + DynamicBox[Manipulate`ManipulateBoxes[ + 1, StandardForm, + "Variables" :> {$CellContext`\:1450\:1455$$ = 4, $CellContext`M$$ = + 0, $CellContext`\[CapitalPi]$$ = + 2, $CellContext`\[CapitalPi]\[CapitalPi]$$ = 8}, + "ControllerVariables" :> {}, + "OtherVariables" :> { + Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, + Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, + Typeset`specs$$, Typeset`size$$, Typeset`update$$, + Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Column[{ + $CellContext`CurvaturePlot[ + Evaluate[ + SetPrecision[ + + SetAccuracy[(1 - 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This section may also include numbered snapshot captions (e.g., \ +Snapshot 1: phrase or sentence without an initial capital and without a \ +period, unless more than one sentence is used) and explanations of the ", + StyleBox["Manipulate", "MRbig"], + " control labels. Define any symbols undefined so far. Include only \ +text in this section \[LongDash] no code, graphics, etc. Do not change the \ +cell style or copy cells from other sections. \n\nA book reference uses this \ +format: \n L. D. Schmidt, ", + StyleBox[ + "The Engineering of Chemical Reactions", FontSlant -> "Italic"], + ", New York: Oxford University Press, 1998. \n\nAn article \ +reference uses this format: \n D. 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Categories are added after the Demonstration is \ +submitted, so the best things to enter here are terms (including any \ +synonyms) that refer to specific parts of the Demonstration. 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