(* 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[ 61299, 1800] NotebookOptionsPosition[ 58424, 1695] NotebookOutlinePosition[ 58922, 1715] CellTagsIndexPosition[ 58879, 1712] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[StyleBox["Normal modes of Nicolium", FontColor->RGBColor[0, 0, 1]]], "Title", CellChangeTimes->{3.568694587110198*^9}], Cell[TextData[{ "Note added 31 January 2013: These animations were constructed 12 October \ 2007 to illustrate the normal modes of a molecule studied by a Chem-Physics \ major named Nicole.\n\nREMARK: Go to the ", StyleBox["Evaluation", FontWeight->"Bold"], " menu and click on ", StyleBox["Evaluate Noteboo", FontWeight->"Bold"], "k. To launch the animations, punch the + tab on the right end of the lower \ slide and hit the start button (\[FilledUpTriangle]).\n" }], "Text", CellChangeTimes->{{3.568694371494207*^9, 3.5686945222862988`*^9}, 3.568694579962232*^9, {3.57092832910769*^9, 3.570928390122142*^9}}], Cell[CellGroupData[{ Cell["Axial countermotion: ", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[Omega]", "=", "2"}]], "Input"], Cell[BoxData["2"], "Output", CellChangeTimes->{3.568693581009506*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"frame1", "[", RowBox[{"a_", ",", "n_"}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1.5`", ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "1.5`"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5`"}], ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5`"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "-", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ")"}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", RowBox[{"(", RowBox[{"1", "-", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ")"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"frame1", "[", RowBox[{".1", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5686940481759157`*^9, 3.568694051840687*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 7.910676956176758, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 20}}, Typeset`size$$ = {176., {3., 10.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$4156$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$4156$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`frame1[0.1, $CellContext`n$$], "Specifications" :> {{$CellContext`n$$, 0, 20}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{313., {58.21875, 64.78125}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.56869405779191*^9, 3.56869407559344*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Rowing 1: ", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[Omega]", "=", RowBox[{ RowBox[{"5", "-", SqrtBox["5"]}], "//", "N"}]}]], "Input"], Cell[BoxData["2.76393202250021`"], "Output", CellChangeTimes->{3.568693581966979*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"frame2", "[", RowBox[{"a_", ",", "n_"}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1.5`", ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "1.5`"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5`"}], ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5`"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "+", SqrtBox["5"]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"5", "-", SqrtBox["5"]}], ")"}]}]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"5", "-", SqrtBox["5"]}], ")"}]}]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"frame2", "[", RowBox[{".1", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{ 3.568693638464488*^9, {3.568693712415468*^9, 3.568693719399768*^9}, { 3.568693827415429*^9, 3.5686938513326693`*^9}, {3.5686938854953127`*^9, 3.568693888671465*^9}, {3.568693931950963*^9, 3.568693953679386*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 15.880355834960938`, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 20}}, Typeset`size$$ = {176., {3., 10.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$4129$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$4129$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`frame2[0.1, $CellContext`n$$], "Specifications" :> {{$CellContext`n$$, 0, 20}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{313., {58.21875, 64.78125}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.5686939616548347`*^9, 3.568693973479327*^9}, 3.5686940051527863`*^9, {3.568694084904161*^9, 3.5686941147766438`*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Rowing 2: ", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[Omega]", "=", RowBox[{ RowBox[{"5", "-", SqrtBox["5"]}], "//", "N"}]}]], "Input"], Cell[BoxData["2.76393202250021`"], "Output", CellChangeTimes->{3.56869358237602*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"frame3", "[", RowBox[{"a_", ",", "n_"}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1.5`", ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "1.5`"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5`"}], ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5`"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "+", SqrtBox["5"]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"5", "-", SqrtBox["5"]}], ")"}]}]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}], ",", "1"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"5", "-", SqrtBox["5"]}], ")"}]}]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}], ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"frame3", "[", RowBox[{".1", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.568694132257695*^9, 3.568694135795066*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 12.501808166503906`, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 20}}, Typeset`size$$ = {176., {3., 10.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$4179$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$4179$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`frame3[0.1, $CellContext`n$$], "Specifications" :> {{$CellContext`n$$, 0, 20}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{313., {58.21875, 64.78125}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.56869414114363*^9, 3.568694155800123*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Vertex countermotion: ", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[Omega]", "=", "4"}]], "Input"], Cell[BoxData["4"], "Output", CellChangeTimes->{3.568693582718322*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"frame4", "[", RowBox[{"a_", ",", "n_"}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1.5`", ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "1.5`"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5`"}], ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5`"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", RowBox[{ RowBox[{"-", "a"}], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "a"}], " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}], ",", "1"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}], ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"frame4", "[", RowBox[{".1", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.5686941697078857`*^9, 3.568694173633062*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 16.742752075195312`, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 20}}, Typeset`size$$ = {176., {3., 10.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$4202$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$4202$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`frame4[0.1, $CellContext`n$$], "Specifications" :> {{$CellContext`n$$, 0, 20}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{313., {58.21875, 64.78125}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.5686941788204403`*^9, 3.568694194784994*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Breathing mode: ", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[Omega]", "=", "6"}]], "Input"], Cell[BoxData["6"], "Output", CellChangeTimes->{3.568693583016362*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"frame5", "[", RowBox[{"a_", ",", "n_"}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1.5`", ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "1.5`"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5`"}], ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5`"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ")"}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", RowBox[{"(", RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ")"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"frame5", "[", RowBox[{".1", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.568694204662768*^9, 3.568694213654726*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 11.453479766845703`, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 20}}, Typeset`size$$ = {176., {3., 10.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$4225$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$4225$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`frame5[0.1, $CellContext`n$$], "Specifications" :> {{$CellContext`n$$, 0, 20}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{313., {58.21875, 64.78125}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.568694218048957*^9, 3.568694231649898*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Jumping jack 1:", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[Omega]", "=", RowBox[{ RowBox[{"5", "+", SqrtBox["5"]}], "//", "N"}]}]], "Input"], Cell[BoxData["7.23606797749979`"], "Output", CellChangeTimes->{3.56869358354661*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"frame6", "[", RowBox[{"a_", ",", "n_"}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1.5`", ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "1.5`"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5`"}], ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5`"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"(", RowBox[{"1", "-", SqrtBox["5"]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"5", "+", SqrtBox["5"]}], ")"}]}]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"5", "+", SqrtBox["5"]}], ")"}]}]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"frame6", "[", RowBox[{".1", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.568694250943201*^9, 3.568694254735468*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 6.524599075317383, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 20}}, Typeset`size$$ = {167., {3., 10.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$4248$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$4248$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`frame6[0.1, $CellContext`n$$], "Specifications" :> {{$CellContext`n$$, 0, 20}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{313., {58.21875, 64.78125}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.568694265876009*^9, 3.568694277510701*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Jumping jack 2: ", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[Omega]", "=", RowBox[{ RowBox[{"5", "+", SqrtBox["5"]}], "//", "N"}]}]], "Input"], Cell[BoxData["7.23606797749979`"], "Output", CellChangeTimes->{3.5686935838352222`*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"frame7", "[", RowBox[{"a_", ",", "n_"}], "]"}], ":=", RowBox[{"Show", "[", RowBox[{ RowBox[{"Graphics", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1.5`", ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", "1.5`"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5`"}], ",", "0"}], "}"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "1", ",", "1"}], "]"}], ",", RowBox[{"Point", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1.5`"}]}], "}"}], "]"}]}], "}"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0"}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"Circle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.1`"}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "-", SqrtBox["5"]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"5", "+", SqrtBox["5"]}], ")"}]}]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}], ",", "1"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}]}], ",", "0"}], "}"}], ",", "0.08`"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"RGBColor", "[", RowBox[{"1", ",", "0", ",", "0"}], "]"}], ",", RowBox[{"Disk", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", RowBox[{ FractionBox["1", "2"], " ", RowBox[{"(", RowBox[{"5", "+", SqrtBox["5"]}], ")"}]}]}], ")"}], " ", "a", " ", RowBox[{"Sin", "[", FractionBox[ RowBox[{"2", " ", "\[Pi]", " ", "n"}], "21"], "]"}]}], ",", RowBox[{"-", "1"}]}], "}"}], ",", "0.08`"}], "]"}]}], "}"}]}], "}"}], "]"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"frame7", "[", RowBox[{".1", ",", "n"}], "]"}], ",", RowBox[{"{", RowBox[{"n", ",", "0", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.568694292803494*^9, 3.568694299248932*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`n$$ = 2.2245655059814453`, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`n$$], 0, 20}}, Typeset`size$$ = {176., {3., 10.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$4271$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`n$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$4271$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> $CellContext`frame7[0.1, $CellContext`n$$], "Specifications" :> {{$CellContext`n$$, 0, 20}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{313., {58.21875, 64.78125}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.568694304557322*^9, 3.568694316462512*^9}}] }, Open ]] }, Open ]] }, Open ]] }, WindowSize->{776, 787}, WindowMargins->{{67, Automatic}, {-61, Automatic}}, DockedCells->(FrontEndExecute[{ FrontEnd`NotebookApply[ FrontEnd`InputNotebook[], #, Placeholder]}]& ), ShowSelection->True, Magnification->1.25, FrontEndVersion->"7.0 for Mac OS X PowerPC (32-bit) (November 11, 2008)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 134, 2, 95, "Title"], Cell[704, 26, 626, 13, 126, "Text"], Cell[CellGroupData[{ Cell[1355, 43, 41, 0, 57, "Subtitle"], Cell[CellGroupData[{ Cell[1421, 47, 56, 1, 33, "Input"], Cell[1480, 50, 70, 1, 33, "Output"] }, Open ]], Cell[1565, 54, 5611, 163, 427, "Input"], Cell[CellGroupData[{ Cell[7201, 221, 274, 7, 33, "Input"], Cell[7478, 230, 1551, 32, 143, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[9078, 268, 30, 0, 57, "Subtitle"], Cell[CellGroupData[{ Cell[9133, 272, 118, 4, 40, "Input"], Cell[9254, 278, 86, 1, 33, "Output"] }, Open ]], Cell[9355, 282, 6283, 180, 452, "Input"], Cell[CellGroupData[{ Cell[15663, 466, 447, 10, 33, "Input"], Cell[16113, 478, 1633, 33, 143, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[17795, 517, 30, 0, 57, "Subtitle"], Cell[CellGroupData[{ Cell[17850, 521, 118, 4, 40, "Input"], Cell[17971, 527, 85, 1, 33, "Output"] }, Open ]], Cell[18071, 531, 6281, 180, 452, "Input"], Cell[CellGroupData[{ Cell[24377, 715, 272, 7, 33, "Input"], Cell[24652, 724, 1554, 32, 143, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[26255, 762, 42, 0, 57, "Subtitle"], Cell[CellGroupData[{ Cell[26322, 766, 56, 1, 33, "Input"], Cell[26381, 769, 70, 1, 33, "Output"] }, Open ]], Cell[26466, 773, 5403, 157, 427, "Input"], Cell[CellGroupData[{ Cell[31894, 934, 274, 7, 33, "Input"], Cell[32171, 943, 1557, 32, 143, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[33777, 981, 36, 0, 57, "Subtitle"], Cell[CellGroupData[{ Cell[33838, 985, 56, 1, 33, "Input"], Cell[33897, 988, 70, 1, 33, "Output"] }, Open ]], Cell[33982, 992, 5611, 163, 427, "Input"], Cell[CellGroupData[{ Cell[39618, 1159, 272, 7, 33, "Input"], Cell[39893, 1168, 1555, 32, 143, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[41497, 1206, 35, 0, 57, "Subtitle"], Cell[CellGroupData[{ Cell[41557, 1210, 118, 4, 40, "Input"], Cell[41678, 1216, 85, 1, 33, "Output"] }, Open ]], Cell[41778, 1220, 6283, 180, 452, "Input"], Cell[CellGroupData[{ Cell[48086, 1404, 272, 7, 33, "Input"], Cell[48361, 1413, 1553, 32, 143, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[49963, 1451, 36, 0, 57, "Subtitle"], Cell[CellGroupData[{ Cell[50024, 1455, 118, 4, 40, "Input"], Cell[50145, 1461, 88, 1, 33, "Output"] }, Open ]], Cell[50248, 1465, 6281, 180, 452, "Input"], Cell[CellGroupData[{ Cell[56554, 1649, 272, 7, 33, "Input"], Cell[56829, 1658, 1555, 32, 143, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)