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Hold[$CellContext`seed$$, $CellContext`seed$201865$$, 0], Hold[$CellContext`pr$$, $CellContext`pr$201866$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`rn$, $CellContext`rnmax$}, {$CellContext`rn$, \ $CellContext`rnmax$} = Map[FoldList[ Plus, {0, 0, 0}, SeedRandom[$CellContext`seed$$]; RandomChoice[ Flatten[ ({#, -#}& )[ Permutations[{0, 0, 1}]], 1], #]]& , {$CellContext`n$$, $CellContext`max$$}]; Graphics3D[ Line[$CellContext`rn$], PlotRange -> If[$CellContext`pr$$, All, Map[{Min[#] - 2, Max[#] + 2}& , Transpose[$CellContext`rnmax$]]], ImageSize -> {500, 350}, BoxStyle -> Dotted]], "Specifications" :> {{{$CellContext`max$$, 10000, "maximum steps"}, { 100, 1000, 10000, 100000}}, {{$CellContext`n$$, 50, "steps taken"}, 1, Dynamic[$CellContext`max$$], 1, Appearance -> "Labeled"}, Delimiter, {{$CellContext`seed$$, 1234, "new random walk"}, 1000, 100000, 1}, {{$CellContext`pr$$, False, "shrink to fit"}, { True, False}}}, "Options" :> {ControllerLinking -> False}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{549., {262., 267.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->154948194] }, {2}]] }, Open ]], Cell[CellGroupData[{ Cell["", "ManipulateCaptionSection"], Cell["\<\ At each step, the walk goes randomly a unit distance along one of the six \ possible 3D coordinate directions. \ \>", "ManipulateCaption", CellChangeTimes->{ 3.35696210375764*^9, {3.3714320211033144`*^9, 3.371432070698017*^9}}, CellID->70610328] }, Open ]], Cell[CellGroupData[{ Cell["", 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{$CellContext`max$$ = 10000, $CellContext`n$$ = 9974, $CellContext`pr$$ = False, $CellContext`seed$$ = 18548}, "ControllerVariables" :> { Hold[$CellContext`max$$, $CellContext`max$201932$$, 0], Hold[$CellContext`n$$, $CellContext`n$201933$$, 0], Hold[$CellContext`seed$$, $CellContext`seed$201934$$, 0], Hold[$CellContext`pr$$, $CellContext`pr$201935$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`rn$, $CellContext`rnmax$}, {$CellContext`rn$, \ $CellContext`rnmax$} = Map[FoldList[ Plus, {0, 0, 0}, SeedRandom[$CellContext`seed$$]; RandomChoice[ Flatten[ ({#, -#}& )[ Permutations[{0, 0, 1}]], 1], #]]& , {$CellContext`n$$, $CellContext`max$$}]; Graphics3D[ Line[$CellContext`rn$], PlotRange -> If[$CellContext`pr$$, All, Map[{Min[#] - 2, Max[#] + 2}& , Transpose[$CellContext`rnmax$]]], ImageSize -> {500, 350}, BoxStyle -> Dotted]], "Specifications" :> {{{$CellContext`max$$, 10000, "maximum steps"}, { 100, 1000, 10000, 100000}}, {{$CellContext`n$$, 9974, "steps taken"}, 1, Dynamic[$CellContext`max$$], 1, Appearance -> "Labeled"}, Delimiter, {{$CellContext`seed$$, 18548, "new random walk"}, 1000, 100000, 1}, {{$CellContext`pr$$, False, "shrink to fit"}, { True, False}}}, "Options" :> {ControllerLinking -> False}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{549., {262., 267.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->488238415] }, Open ]], Cell[CellGroupData[{ Cell["", "SnapshotsSection"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`max$$ = 10000, 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10000, "maximum steps"}, { 100, 1000, 10000, 100000}}, {{$CellContext`n$$, 10000, "steps taken"}, 1, Dynamic[$CellContext`max$$], 1, Appearance -> "Labeled"}, Delimiter, {{$CellContext`seed$$, 1234, "new random walk"}, 1000, 100000, 1}, {{$CellContext`pr$$, False, "shrink to fit"}, { True, False}}}, "Options" :> {ControllerLinking -> False}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{549., {262., 267.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->706327172], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`max$$ = 10000, $CellContext`n$$ = 10000, $CellContext`pr$$ = False, $CellContext`seed$$ = 46833, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 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Delimiter, {{$CellContext`seed$$, 46833, "new random walk"}, 1000, 100000, 1}, {{$CellContext`pr$$, False, "shrink to fit"}, { True, False}}}, "Options" :> {ControllerLinking -> False}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{549., {262., 267.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->268898523], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`max$$ = 10000, $CellContext`n$$ = 10000, $CellContext`pr$$ = False, $CellContext`seed$$ = 82976, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`max$$], 10000, "maximum steps"}, {100, 1000, 10000, 100000}}, {{ Hold[$CellContext`n$$], 10000, "steps taken"}, 1, Dynamic[$CellContext`max$$], 1}, {{ Hold[$CellContext`seed$$], 82976, "new random walk"}, 1000, 100000, 1}, {{ Hold[$CellContext`pr$$], False, "shrink to fit"}, {True, False}}}, Typeset`size$$ = {500., {173., 177.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`max$202139$$ = 0, $CellContext`n$202140$$ = 0, $CellContext`seed$202141$$ = 0, $CellContext`pr$202142$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`max$$ = 10000, $CellContext`n$$ = 10000, $CellContext`pr$$ = False, $CellContext`seed$$ = 82976}, "ControllerVariables" :> { Hold[$CellContext`max$$, $CellContext`max$202139$$, 0], Hold[$CellContext`n$$, $CellContext`n$202140$$, 0], Hold[$CellContext`seed$$, $CellContext`seed$202141$$, 0], Hold[$CellContext`pr$$, $CellContext`pr$202142$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`rn$, $CellContext`rnmax$}, {$CellContext`rn$, \ $CellContext`rnmax$} = Map[FoldList[ Plus, {0, 0, 0}, SeedRandom[$CellContext`seed$$]; RandomChoice[ Flatten[ ({#, -#}& )[ Permutations[{0, 0, 1}]], 1], #]]& , {$CellContext`n$$, $CellContext`max$$}]; Graphics3D[ Line[$CellContext`rn$], PlotRange -> If[$CellContext`pr$$, All, Map[{Min[#] - 2, Max[#] + 2}& , Transpose[$CellContext`rnmax$]]], ImageSize -> {500, 350}, BoxStyle -> Dotted]], "Specifications" :> {{{$CellContext`max$$, 10000, "maximum steps"}, { 100, 1000, 10000, 100000}}, {{$CellContext`n$$, 10000, "steps taken"}, 1, Dynamic[$CellContext`max$$], 1, Appearance -> "Labeled"}, Delimiter, {{$CellContext`seed$$, 82976, "new random walk"}, 1000, 100000, 1}, {{$CellContext`pr$$, False, "shrink to fit"}, { True, False}}}, "Options" :> {ControllerLinking -> False}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{549., {262., 267.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->152843064] }, Open ]], Cell["", "DetailsSection"], Cell[CellGroupData[{ Cell["", "ControlSuggestionsSection"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[True], Cell[" Resize Images"]}], "\"Click inside an image to reveal its orange resize frame.\\nDrag any of \ the orange resize handles to resize the image.\"", TooltipDelay->0.35]], "ControlSuggestions", FontFamily->"Verdana", CellTags->"ResizeImages"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[True], Cell[" Rotate and Zoom in 3D"]}], RowBox[{ "\"Drag a 3D graphic to rotate it. Starting the drag near the center \ tumbles\\nthe graphic; starting near a corner turns it parallel to the plane \ of the screen.\\nHold down \"", FrameBox[ "Ctrl", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" (or \"", FrameBox[ "Cmd", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" on Mac) and drag up and down to zoom.\""}], TooltipDelay->0.35]], "ControlSuggestions", FontFamily->"Verdana", CellTags->"RotateAndZoomIn3D"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[False], Cell[" Drag Locators"]}], RowBox[{"\"Drag any locator (\"", GraphicsBox[ LocatorBox[ Scaled[{0.5, 0.5}]], ImageSize -> 20], "\", etc.) to move it around.\""}], TooltipDelay->0.35]], "ControlSuggestions", FontFamily->"Verdana", CellTags->"DragLocators"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[False], Cell[" Create and Delete Locators"]}], RowBox[{"\"Insert a new locator in the graphic by holding down the \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" key\\nand clicking where you want it to be. Delete a locator by \ clicking it\\nwhile holding down the \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" key.\""}], TooltipDelay->0.35]], "ControlSuggestions", FontFamily->"Verdana", CellTags->"CreateAndDeleteLocators"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[True], Cell[" Slider Zoom"]}], RowBox[{"\"Hold down the \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" key while moving a slider to make fine adjustments in the slider \ value.\\nHold \"", FrameBox[ "Ctrl", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" and/or \"", FrameBox[ "Shift", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" at the same time as \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" to make ever finer adjustments.\""}], TooltipDelay->0.35]], "ControlSuggestions", 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