O
/
OO
0
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
OO/𖣠⚪∣❁∣ᙁᑐᑕ∣옷⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪.../⚪ᕤᕦ⚪ИN⚪ꖴ⚪✤⚪ᑎ⚪ߦ⚪ᙏ⚪Ⓞ⚪ᑐᑕ⚪◌⚪◌⚪◌.../⚪ᗱᗴ⚪ᴥ⚪ᗩ⚪ᗯ⚪✤⚪ꗳ⚪Ⓞ⚪ᔓᔕ⚪◌⚪◌⚪◌⚪◌⚪.../⚪ᙏ⚪ᗩ⚪ᴥ⚪ꗳ⚪ᙁ⚪Ⓞ⚪ᗯ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪.../⚪ᗩ⚪ᑐᑕ⚪ꖴ⚪✤⚪ᗩ⚪ᙏ⚪ᗱᗴ⚪옷⚪✤⚪ᗩ⚪ᙏ⚪◌⚪.../ᗺИ.𖣠⚪𔗢⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᗩ⚪ᴥ⚪✤⚪ᔓᔕ⚪ИN...

1977 lines
84 KiB
Plaintext
Raw Normal View History

ᗺИ.𖣠⚪𔗢⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᗩ⚪ᙁ⚪ᑎ⚪ߦ⚪ꖴ⚪ИN⚪ᗩ⚪ᙏ⚪𖣓⚪ᗱᗴ⚪ᴥ⚪ᑎ⚪✤⚪ᗩ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪𔗢⚪𓊗⚪𔗢⚪𖣠⚪𔗢⚪𖡼⚪𔗢⚪𖣠⚪𔗢⚪𖡼⚪𔗢⚪𖣠⚪𔗢⚪𖡼⚪𔗢⚪𖣠⚪𔗢⚪𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼⚪𔗢⚪𖣠⚪𔗢⚪𖡼⚪𔗢⚪𖣠⚪𔗢⚪𖡼⚪𔗢⚪𖣠⚪𔗢⚪𖡼⚪𔗢⚪𖣠⚪𔗢⚪𓊗⚪𔗢⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗩ⚪✤⚪ᑎ⚪ᴥ⚪ᗱᗴ⚪𖣓⚪ᙏ⚪ᗩ⚪ИN⚪ꖴ⚪ߦ⚪ᑎ⚪ᙁ⚪ᗩ⚪✤⚪ꖴ⚪Ⓞ⚪ИN⚪𔗢⚪𖣠.NB
2024-03-24 14:43:02 +00:00
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 12.2' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 84233, 1968]
NotebookOptionsPosition[ 74111, 1767]
NotebookOutlinePosition[ 80482, 1901]
CellTagsIndexPosition[ 79828, 1879]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["\<\
\|0168e0\:26aa\|0145e2\:26aa\:0418N\:26aa\:24c4\:26aa\:a5b4\:26aa\:2724\:26aa\
\:15e9\:26aa\:1641\:26aa\:144e\:26aa\:07e6\:26aa\:a5b4\:26aa\:0418N\:26aa\
\:15e9\:26aa\:164f\:26aa\:25ef\:26aa\:15f1\:15f4\:26aa\:1d25\:26aa\:144e\:26aa\
\:2724\:26aa\:15e9\:26aa\:15ef\:26aa\:1d25\:26aa\:144e\:26aa\:1450\:1455\:26aa\
\|0145e2\:26aa\|013297\:26aa\|0145e2\:26aa\|0168e0\:26aa\|0145e2\:26aa\|01687c\
\:26aa\|0145e2\:26aa\|0168e0\:26aa\|0145e2\:26aa\|01687c\:26aa\|0145e2\:26aa\
\|0168e0\:26aa\|0145e2\:26aa\|01687c\:26aa\|0145e2\:26aa\|0168e0\:26aa\|0145e2\
\:26aa\|01687c\:26aa\|0145e2\:26aa\|01f78b\:26aa\|0145e2\:26aa\|01687c\:26aa\
\|0145e2\:26aa\|0168e0\:26aa\|0145e2\:26aa\|01687c\:26aa\|0145e2\:26aa\|0168e0\
\:26aa\|0145e2\:26aa\|01687c\:26aa\|0145e2\:26aa\|0168e0\:26aa\|0145e2\:26aa\
\|01687c\:26aa\|0145e2\:26aa\|0168e0\:26aa\|0145e2\:26aa\|013297\:26aa\|0145e2\
\:26aa\:1450\:1455\:26aa\:144e\:26aa\:1d25\:26aa\:15ef\:26aa\:15e9\:26aa\:2724\
\:26aa\:144e\:26aa\:1d25\:26aa\:15f1\:15f4\:26aa\:25ef\:26aa\:164f\:26aa\:15e9\
\:26aa\:0418N\:26aa\:a5b4\:26aa\:07e6\:26aa\:144e\:26aa\:1641\:26aa\:15e9\
\:26aa\:2724\:26aa\:a5b4\:26aa\:24c4\:26aa\:0418N\:26aa\|0145e2\:26aa\|0168e0\
\>", "Title",
CellChangeTimes->{{3.920280967590807*^9, 3.920280977878854*^9}},
TextAlignment->Center,
FontFamily->"Go Noto Ancient",
FontSize->9,
FontWeight->"Normal",
FontTracking->"Plain",ExpressionUUID->"b9e6fe14-67c5-4f7d-9ec0-13c361826e91"],
Cell[CellGroupData[{
Cell[TextData[{
"Initialization Code",
StyleBox[" (optional) ", "SectionGloss"],
Cell[BoxData[
TemplateBox[{"Initialization Code",
Cell[
BoxData[
FrameBox[
Cell[
TextData[{"Provide any code that must be evaluated before the ",
StyleBox["Manipulate", "MRbig"],
". This will automatically be built into the ",
StyleBox["Manipulate", "MRbig"],
" in the final notebook version. Never use a package that is not \
included in the default distribution of ",
StyleBox["Mathematica", FontSlant -> "Italic"],
". To use a package, use the ",
StyleBox["Initialization", "MRbig"], " option (with ",
StyleBox["Get", "MRbig"], ", not ",
StyleBox["Needs", "MRbig"], ") in the ",
StyleBox["Manipulate", "MRbig"],
" itself, and use the full name of the function from the package. \
For example:\n",
StyleBox[
" Manipulate[\n ...\n ComputationalGeometry`ConvexHull[...]...\n \
...\n Initialization :> Get[\"ComputationalGeometry`\"],\n ...\n ]",
"MR"], "\nIf you provide initialization code, include a ",
StyleBox["SaveDefinitions->True", "MRbig"], " option in the ",
StyleBox["Manipulate", "MRbig"], ".",
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->
"81fde376-e763-44cf-83ed-5c52ec315067"]
}], "InitializationSection",
TextAlignment->Center,
CellTags->
"Initialization \
Code",ExpressionUUID->"1d34a731-8c48-4189-8b6f-89ef5777db9f"],
Cell[BoxData[{
RowBox[{"ClearAll", "[",
RowBox[{"iCurvaturePlotHelper", ",", "CurvaturePlot"}], "]"}], "\n",
RowBox[{
RowBox[{"iCurvaturePlotHelper", "[",
RowBox[{
RowBox[{"f_", "?",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"Head", "[", "#", "]"}], "=!=", "List"}], "&"}], ")"}]}], ",",
RowBox[{"{",
RowBox[{"t_", ",", "tmin_", ",", "tmax_"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"x0_", ",", "y0_"}], "}"}], ",", "\[Theta]0_"}], "}"}], ",",
RowBox[{"opts", ":",
RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], ":=",
RowBox[{"Module", "[",
RowBox[{
RowBox[{"{",
RowBox[{"sol", ",", "\[Theta]", ",", "x", ",", "y", ",", "if"}], "}"}],
",",
RowBox[{
RowBox[{"sol", "=",
RowBox[{"NDSolve", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"\[Theta]", "'"}], "[", "t", "]"}], "\[Equal]", "f"}],
",",
RowBox[{
RowBox[{
RowBox[{"x", "'"}], "[", "t", "]"}], "\[Equal]",
RowBox[{"Cos", "[",
RowBox[{"\[Theta]", "[", "t", "]"}], "]"}]}], ",",
RowBox[{
RowBox[{
RowBox[{"y", "'"}], "[", "t", "]"}], "\[Equal]",
RowBox[{"Sin", "[",
RowBox[{"\[Theta]", "[", "t", "]"}], "]"}]}], ",",
RowBox[{
RowBox[{"\[Theta]", "[", "tmin", "]"}], "\[Equal]", "\[Theta]0"}],
",",
RowBox[{
RowBox[{"x", "[", "tmin", "]"}], "\[Equal]", "x0"}], ",",
RowBox[{
RowBox[{"y", "[", "tmin", "]"}], "\[Equal]", "y0"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "y"}], "}"}], ",",
RowBox[{"{",
RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}], ",", "opts"}],
"]"}]}], ";", "\[IndentingNewLine]",
RowBox[{"if", "=",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"x", "[", "#", "]"}], ",",
RowBox[{"y", "[", "#", "]"}]}], "}"}], "&"}], "/.", " ",
RowBox[{"First", "[", "sol", "]"}]}]}], ";", "\[IndentingNewLine]",
"if"}]}], "]"}]}], "\n",
RowBox[{
RowBox[{"CurvaturePlot", "[",
RowBox[{"f_", ",",
RowBox[{"{",
RowBox[{"t_", ",", "tmin_", ",", "tmax_"}], "}"}], ",",
RowBox[{"opts", ":",
RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], ":=",
RowBox[{"CurvaturePlot", "[",
RowBox[{"f", ",",
RowBox[{"{",
RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "0"}], "}"}], ",", "0"}], "}"}], ",", "opts"}],
"]"}]}], "\n",
RowBox[{
RowBox[{"CurvaturePlot", "[",
RowBox[{"f_", ",",
RowBox[{"{",
RowBox[{"t_", ",", "tmin_", ",", "tmax_"}], "}"}], ",",
RowBox[{"p", ":",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"x0_", ",", "y0_"}], "}"}], ",", "\[Theta]0_"}], "}"}]}], ",",
RowBox[{"opts", ":",
RowBox[{"OptionsPattern", "[", "]"}]}]}], "]"}], ":=",
RowBox[{"Module", "[",
RowBox[{
RowBox[{"{",
RowBox[{
"\[Theta]", ",", "x", ",", "y", ",", "sol", ",", "rlsplot", ",",
"rlsndsolve", ",", "if", ",", "ifs"}], "}"}], ",",
RowBox[{
RowBox[{"rlsplot", "=",
RowBox[{"FilterRules", "[",
RowBox[{
RowBox[{"{", "opts", "}"}], ",",
RowBox[{"Options", "[", "ParametricPlot", "]"}]}], "]"}]}], ";",
"\[IndentingNewLine]",
RowBox[{"rlsndsolve", "=",
RowBox[{"FilterRules", "[",
RowBox[{
RowBox[{"{", "opts", "}"}], ",",
RowBox[{"Options", "[", "NDSolve", "]"}]}], "]"}]}], ";",
"\[IndentingNewLine]",
RowBox[{"If", "[",
RowBox[{
RowBox[{
RowBox[{"Head", "[", "f", "]"}], "===", "List"}], ",",
RowBox[{
RowBox[{"ifs", "=",
RowBox[{
RowBox[{
RowBox[{"iCurvaturePlotHelper", "[",
RowBox[{"#", ",",
RowBox[{"{",
RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}], ",", "p", ",",
RowBox[{"Evaluate", "@",
RowBox[{"(",
RowBox[{"Sequence", "@@", "rlsndsolve"}], ")"}]}]}], "]"}],
"&"}], "/@", "f"}]}], ";", "\[IndentingNewLine]",
RowBox[{"ParametricPlot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{
RowBox[{
RowBox[{"#", "[", "tplot", "]"}], "&"}], "/@", "ifs"}], "]"}],
",",
RowBox[{"{",
RowBox[{"tplot", ",", "tmin", ",", "tmax"}], "}"}], ",",
RowBox[{"Evaluate", "@",
RowBox[{"(",
RowBox[{"Sequence", "@@", "rlsplot"}], ")"}]}]}], "]"}]}], ",",
RowBox[{
RowBox[{"if", "=",
RowBox[{"iCurvaturePlotHelper", "[",
RowBox[{"f", ",",
RowBox[{"{",
RowBox[{"t", ",", "tmin", ",", "tmax"}], "}"}], ",", "p", ",",
RowBox[{"Evaluate", "@",
RowBox[{"(",
RowBox[{"Sequence", "@@", "rlsndsolve"}], ")"}]}]}], "]"}]}],
";", "\[IndentingNewLine]",
RowBox[{"ParametricPlot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{"if", "[", "tplot", "]"}], "]"}], ",",
RowBox[{"{",
RowBox[{"tplot", ",", "tmin", ",", "tmax"}], "}"}], ",",
RowBox[{"Evaluate", "@",
RowBox[{"(",
RowBox[{"Sequence", "@@", "rlsplot"}], ")"}]}]}], "]"}]}]}],
"]"}]}]}], "]"}]}]}], "Input",
CellChangeTimes->{{3.920278406604987*^9, 3.9202784080949893`*^9}},
TextAlignment->Center,
CellLabel->"3/24/24 16:39:37 In[1]:=",
CellID->24701595,ExpressionUUID->"ee244b7a-a530-47db-8602-9dbd7bcdc504"],
Cell[BoxData[{
RowBox[{
RowBox[{
RowBox[{"ariasD", "[", "0", "]"}], " ", "=", " ", "1"}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"ariasD", "[",
RowBox[{"n_Integer", "?", "Positive"}], "]"}], " ", ":=", " ",
RowBox[{
RowBox[{"ariasD", "[", "n", "]"}], " ", "=", " ",
RowBox[{
RowBox[{"Sum", "[",
RowBox[{
RowBox[{
RowBox[{"2", "^",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"k", " ",
RowBox[{"(",
RowBox[{"k", " ", "-", " ", "1"}], ")"}]}], " ", "-", " ",
RowBox[{"n", " ",
RowBox[{"(",
RowBox[{"n", " ", "-", " ", "1"}], ")"}]}]}], ")"}], "/",
"2"}], ")"}]}], " ",
RowBox[{
RowBox[{"ariasD", "[", "k", "]"}], "/",
RowBox[{
RowBox[{"(",
RowBox[{"n", " ", "-", " ", "k", " ", "+", " ", "1"}], ")"}],
"!"}]}]}], ",", " ",
RowBox[{"{",
RowBox[{"k", ",", " ", "0", ",", " ",
RowBox[{"n", " ", "-", " ", "1"}]}], "}"}]}], "]"}], "/",
RowBox[{"(",
RowBox[{
RowBox[{"2", "^", "n"}], " ", "-", " ", "1"}], ")"}]}]}]}],
";"}], "\n",
RowBox[{
RowBox[{"iFabiusF", "[", "x_", "]"}], " ", ":=", " ",
RowBox[{"Module", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"prec", " ", "=", " ",
RowBox[{"Precision", "[", "x", "]"}]}], ",", " ", "n", ",", " ", "p",
",", " ", "q", ",", " ", "s", ",", " ", "tol", ",", " ", "w", ",", " ",
"y", ",", " ", "z"}], "}"}], ",", "\n", " ",
RowBox[{
RowBox[{"If", "[",
RowBox[{
RowBox[{"x", " ", "<", " ", "0"}], ",", " ",
RowBox[{"Return", "[",
RowBox[{"0", ",", " ", "Module"}], "]"}]}], "]"}], ";", " ",
RowBox[{"tol", " ", "=", " ",
RowBox[{"10", "^",
RowBox[{"(",
RowBox[{"-", "prec"}], ")"}]}]}], ";", "\n", " ",
RowBox[{"z", " ", "=", " ",
RowBox[{"SetPrecision", "[",
RowBox[{"x", ",", " ", "Infinity"}], "]"}]}], ";", " ",
RowBox[{"s", " ", "=", " ", "1"}], ";", " ",
RowBox[{"y", " ", "=", " ", "0"}], ";", "\n", " ",
RowBox[{"z", " ", "=", " ",
RowBox[{"If", "[",
RowBox[{
RowBox[{"0", " ", "<=", " ", "z", " ", "<=", " ", "2"}], ",", " ",
RowBox[{"1", " ", "-", " ",
RowBox[{"Abs", "[",
RowBox[{"1", " ", "-", " ", "z"}], "]"}]}], ",", "\n", " ",
RowBox[{
RowBox[{"q", " ", "=", " ",
RowBox[{"Quotient", "[",
RowBox[{"z", ",", " ", "2"}], "]"}]}], ";", "\n", " ",
RowBox[{"If", "[",
RowBox[{
RowBox[{
RowBox[{"ThueMorse", "[", "q", "]"}], " ", "==", " ", "1"}], ",",
" ",
RowBox[{"s", " ", "=", " ",
RowBox[{"-", "1"}]}]}], "]"}], ";", "\n", " ",
RowBox[{"1", " ", "-", " ",
RowBox[{"Abs", "[",
RowBox[{"1", " ", "-", " ", "z", " ", "+", " ",
RowBox[{"2", " ", "q"}]}], "]"}]}]}]}], "]"}]}], ";", "\n", " ",
RowBox[{"While", "[",
RowBox[{
RowBox[{"z", " ", ">", " ", "0"}], ",", "\n", " ",
RowBox[{
RowBox[{"n", " ", "=", " ",
RowBox[{"-",
RowBox[{"Floor", "[",
RowBox[{"RealExponent", "[",
RowBox[{"z", ",", " ", "2"}], "]"}], "]"}]}]}], ";", " ",
RowBox[{"p", " ", "=", " ",
RowBox[{"2", "^", "n"}]}], ";", "\n", " ",
RowBox[{"z", " ", "-=", " ",
RowBox[{"1", "/", "p"}]}], ";", " ",
RowBox[{"w", " ", "=", " ", "1"}], ";", "\n", " ",
RowBox[{"Do", "[",
RowBox[{
RowBox[{
RowBox[{"w", " ", "=", " ",
RowBox[{
RowBox[{"ariasD", "[", "m", "]"}], " ", "+", " ",
RowBox[{"p", " ", "z", " ",
RowBox[{"w", "/",
RowBox[{"(",
RowBox[{"n", " ", "-", " ", "m", " ", "+", " ", "1"}],
")"}]}]}]}]}], ";", " ",
RowBox[{"p", " ", "/=", " ", "2"}]}], ",", " ",
RowBox[{"{",
RowBox[{"m", ",", " ", "n"}], "}"}]}], "]"}], ";", "\n", " ",
RowBox[{"y", " ", "=", " ",
RowBox[{"w", " ", "-", " ", "y"}]}], ";", "\n", " ",
RowBox[{"If", "[",
RowBox[{
RowBox[{
RowBox[{"Abs", "[", "w", "]"}], " ", "<", " ",
RowBox[{
RowBox[{"Abs", "[", "y", "]"}], " ", "tol"}]}], ",", " ",
RowBox[{"Break", "[", "]"}]}], "]"}]}]}], "]"}], ";", "\n", " ",
RowBox[{"SetPrecision", "[",
RowBox[{
RowBox[{"s", " ",
RowBox[{"Abs", "[", "y", "]"}]}], ",", " ", "prec"}], "]"}]}]}],
"]"}]}], "\n",
RowBox[{
RowBox[{
RowBox[{"FabiusF", "[", "Infinity", "]"}], " ", "=", " ",
RowBox[{"Interval", "[",
RowBox[{"{",
RowBox[{
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], "]"}]}], ";"}], "\n",
RowBox[{
RowBox[{
RowBox[{"FabiusF", "[",
RowBox[{"x_", "?", "NumberQ"}], "]"}], " ", "/;", " ",
RowBox[{"If", "[",
RowBox[{
RowBox[{
RowBox[{"Im", "[", "x", "]"}], " ", "==", " ", "0"}], ",", " ",
RowBox[{"TrueQ", "[",
RowBox[{
RowBox[{
RowBox[{"Composition", "[",
RowBox[{
RowBox[{
RowBox[{"BitAnd", "[",
RowBox[{"#", ",", " ",
RowBox[{"#", " ", "-", " ", "1"}]}], "]"}], " ", "&"}], ",", " ",
"Denominator"}], "]"}], "[", "x", "]"}], " ", "==", " ", "0"}],
"]"}], ",", " ", "False"}], "]"}]}], " ", ":=", " ",
RowBox[{"iFabiusF", "[", "x", "]"}]}], "\n",
RowBox[{
RowBox[{
RowBox[{"Derivative", "[", "n_Integer", "]"}], "[", "FabiusF", "]"}], " ",
":=", " ",
RowBox[{
RowBox[{
RowBox[{"2", "^",
RowBox[{"(",
RowBox[{"n", " ",
RowBox[{
RowBox[{"(",
RowBox[{"n", " ", "+", " ", "1"}], ")"}], "/", "2"}]}], ")"}]}], " ",
RowBox[{"FabiusF", "[",
RowBox[{
RowBox[{"2", "^", "n"}], " ", "#"}], "]"}]}], " ", "&"}]}], "\n",
RowBox[{
RowBox[{"SetAttributes", "[",
RowBox[{"FabiusF", ",", " ",
RowBox[{"{",
RowBox[{"NumericFunction", ",", " ", "Listable"}], "}"}]}], "]"}],
";"}]}], "Input",
CellChangeTimes->{{3.920278426655015*^9, 3.9202784413650355`*^9}},
TextAlignment->Center,
CellLabel->"3/24/24 16:39:38 In[5]:=",
CellID->25712845,ExpressionUUID->"c1a65306-27f7-4756-940f-772f9967450d"],
Cell[BoxData[{
RowBox[{
RowBox[{"\:1513\:1515", "=",
RowBox[{"{",
RowBox[{
RowBox[{"WorkingPrecision", "\[Rule]", "10"}], ",",
RowBox[{"MaxRecursion", "\[Rule]", "0"}], ",",
RowBox[{"Ticks", "\[Rule]",
RowBox[{"{",
RowBox[{"Automatic", ",", "Automatic"}], "}"}]}], ",",
RowBox[{"ImageSize", "\[Rule]", "320"}], ",",
RowBox[{"PlotRange", "\[Rule]", "Full"}], ",",
RowBox[{"Frame", "\[Rule]", "True"}], ",",
RowBox[{"Axes", "\[Rule]", "False"}], ",",
RowBox[{"GridLines", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"{", "0", "}"}], ",",
RowBox[{"{", "0", "}"}]}], "}"}]}], ",",
RowBox[{"PlotStyle", "\[Rule]",
RowBox[{"GrayLevel", "[",
RowBox[{"168", "/", "256"}], "]"}]}], ",",
RowBox[{"FrameStyle", "\[Rule]",
RowBox[{"GrayLevel", "[",
RowBox[{"178", "/", "256"}], "]"}]}]}], "}"}]}], ";"}], "\n",
RowBox[{
RowBox[{"\[CapitalPi]", "=", "2"}], ";",
RowBox[{"\:1450\:1455", "=", "4"}], ";",
RowBox[{"M", "=", ".5"}], ";",
RowBox[{"\[CapitalPi]\[CapitalPi]", "=", "4"}], ";"}], "\n",
RowBox[{
RowBox[{"\:15f1\:15f4", "=",
RowBox[{"Evaluate", "[",
RowBox[{"SetPrecision", "[",
RowBox[{
RowBox[{"SetAccuracy", "[",
RowBox[{
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{"Abs", "[",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "^",
RowBox[{"Floor", "[",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"x", "/", "Pi"}], "*", "\:1450\:1455"}], "+",
"1"}], ")"}], "/", "2"}], "]"}]}], " ",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{
RowBox[{"Mod", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"x", "/", "Pi"}], "*", "\:1450\:1455"}], "+",
"1"}], ",", "2"}], "]"}], "-", "1"}], "]"}], "^",
"\[CapitalPi]"}]}], ")"}], "]"}], "^",
RowBox[{"(",
RowBox[{"1", "/", "\[CapitalPi]"}], ")"}]}]}], ")"}], "/",
"2"}], "+", ".5"}], "]"}]}], ")"}], ",", "Infinity"}], "]"}],
",", "Infinity"}], "]"}], "]"}]}], ";"}]}], "Input",
CellChangeTimes->{{3.920278449345047*^9, 3.920278487981105*^9}},
TextAlignment->Center,
CellLabel->"3/24/24 16:39:38 In[12]:=",
CellID->77166300,ExpressionUUID->"8d88b28f-3f47-427b-b865-62c1837375dc"]
}, Open ]],
Cell[CellGroupData[{
Cell[TextData[{
"Manipulate",
Cell[BoxData[
TemplateBox[{"Manipulate",
Cell[
BoxData[
FrameBox[
Cell[
TextData[{"This section contains the ",
StyleBox["Manipulate", "MRbig"],
" input cell and its evaluated output cell. Make all control labels \
or labels in the output as descriptive as possible, with only proper nouns \
and proper adjectives capitalized. More description of the controls can be \
provided in the Details section below, if necessary. If you change this ",
StyleBox["Manipulate", "MRbig"],
" after creating screenshots and/or thumbnails, use ",
StyleBox["Update Thumbnail & Snapshots", FontWeight -> "Bold"],
" in the toolbar to update any copies in later sections. You can \
control the Flash preview for the Demonstration with the ",
StyleBox["AutorunSequencing", "MRbig"], " option. Use ",
StyleBox["SaveDefinitions->True", "MRbig"],
" if you provided initialization code in the previous section."}],
"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->
"d12d57a6-93e6-4518-8a9c-9df2eb688354"]
}], "ManipulateSection",
TextAlignment->Center,
CellTags->
"Manipulate",ExpressionUUID->"b7acceb9-ca4b-4965-b319-bd8a6214a587"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Grid", "[",
RowBox[{"{",
RowBox[{"{",
RowBox[{"Manipulate", "[",
RowBox[{
RowBox[{"Column", "[",
RowBox[{"{",
RowBox[{
RowBox[{"CurvaturePlot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{"SetPrecision", "[",
RowBox[{
RowBox[{"SetAccuracy", "[",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{"Abs", "[",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "^",
RowBox[{"Floor", "[",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"x", "/", "Pi"}], "*", "\:1450\:1455"}], "+",
"1"}], ")"}], "/", "2"}], "]"}]}], " ",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{
RowBox[{"Mod", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"x", "/", "Pi"}], "*", "\:1450\:1455"}], "+",
"1"}], ",", "2"}], "]"}], "-", "1"}], "]"}], "^",
"\[CapitalPi]"}]}], ")"}], "]"}], "^",
RowBox[{"(",
RowBox[{"1", "/", "\[CapitalPi]"}], ")"}]}]}], ")"}], "/",
"2"}], "+", ".5"}], "]"}]}], ")"}], "-", "M"}], ",",
"Infinity"}], "]"}], ",", "Infinity"}], "]"}], "]"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",",
RowBox[{"4", "\[Pi]"}]}], "}"}], ",",
RowBox[{"Evaluate", "[", "\:1513\:1515", "]"}], ",",
RowBox[{"FrameTicks", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"Range", "[",
RowBox[{
RowBox[{"-", "16"}], ",", "16", ",",
RowBox[{"1", "/", "2"}]}], "]"}], ",",
RowBox[{"Range", "[",
RowBox[{
RowBox[{"-", "4"}], ",", "4", ",",
RowBox[{"1", "/", "2"}]}], "]"}]}], "}"}]}], ",",
RowBox[{"PlotPoints", "\[Rule]",
RowBox[{"1", "+",
RowBox[{"2", "^", "\[CapitalPi]\[CapitalPi]"}]}]}]}], "]"}], ",",
RowBox[{"Plot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{"SetPrecision", "[",
RowBox[{
RowBox[{"SetAccuracy", "[",
RowBox[{
RowBox[{".5", "-",
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{"Abs", "[",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"-", "1"}], ")"}], "^",
RowBox[{"Floor", "[",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"x", "/", "Pi"}], "*", "\:1450\:1455"}], "+",
"1"}], ")"}], "/", "2"}], "]"}]}], " ",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{"(",
RowBox[{"1", "-",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{
RowBox[{"Mod", "[",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"x", "/", "Pi"}], "*", "\:1450\:1455"}], "+",
"1"}], ",", "2"}], "]"}], "-", "1"}], "]"}], "^",
"\[CapitalPi]"}]}], ")"}], "]"}], "^",
RowBox[{"(",
RowBox[{"1", "/", "\[CapitalPi]"}], ")"}]}]}], ")"}], "/",
"2"}], "+", ".5"}], "]"}]}], ")"}], "-", "M"}], ",",
"Infinity"}], "]"}], ",", "Infinity"}], "]"}], "]"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",",
RowBox[{"4", "\[Pi]"}]}], "}"}], ",",
RowBox[{"Evaluate", "[", "\:1513\:1515", "]"}], ",",
RowBox[{"AspectRatio", "\[Rule]",
RowBox[{"1", "/", "8"}]}], ",",
RowBox[{"FrameTicks", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"Range", "[",
RowBox[{
RowBox[{
RowBox[{"-", "16"}], "*", "Pi"}], ",",
RowBox[{"16", "*", "Pi"}], ",",
RowBox[{"Pi", "/", "2"}]}], "]"}], ",",
RowBox[{"Range", "[",
RowBox[{
RowBox[{"-", "1"}], ",", "1", ",",
RowBox[{"1", "/", "2"}]}], "]"}]}], "}"}]}], ",",
RowBox[{"PlotPoints", "\[Rule]",
RowBox[{"1", "+",
RowBox[{"2", "^", "\[CapitalPi]\[CapitalPi]"}]}]}]}], "]"}]}],
"}"}], "]"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\[CapitalPi]", ",", "1"}], "}"}], ",", "0", ",", "16", ",",
".25"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\:1450\:1455", ",", "4"}], "}"}], ",", "0", ",", "16", ",",
".25"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"M", ",", "0"}], "}"}], ",", "0", ",", "1", ",", ".125"}],
"}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\[CapitalPi]\[CapitalPi]", ",", "8"}], "}"}], ",", "0", ",",
"16", ",", "1"}], "}"}], ",",
RowBox[{"FrameMargins", "\[Rule]", "0"}]}], "]"}], "}"}], "}"}],
"]"}]], "Input",
CellChangeTimes->{
3.92027849196111*^9, {3.9202811539891205`*^9, 3.9202811542691207`*^9}},
TextAlignment->Center,
CellLabel->
"3/24/24 16:59:26 \
In[16]:=",ExpressionUUID->"1c8a51fe-61b3-446f-b3f3-b27c622b6763"],
Cell[BoxData[
TagBox[GridBox[{
{
TagBox[
StyleBox[
DynamicModuleBox[{$CellContext`\:1450\:1455$$ = 4, $CellContext`M$$ =
0, $CellContext`\[CapitalPi]$$ =
1, $CellContext`\[CapitalPi]\[CapitalPi]$$ = 8, Typeset`show$$ = True,
Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu",
Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ =
"\"untitled\"", Typeset`specs$$ = {{{
Hold[$CellContext`\[CapitalPi]$$], 1}, 0, 16, 0.25}, {{
Hold[$CellContext`\:1450\:1455$$], 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]$$ =
1, $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]$$, 1}, 0, 16,
0.25}, {{$CellContext`\:1450\:1455$$, 4}, 0, 16,
0.25}, {{$CellContext`M$$, 0}, 0, 1,
0.125}, {{$CellContext`\[CapitalPi]\[CapitalPi]$$, 8}, 0, 16,
1}}, "Options" :> {FrameMargins -> 0},
"DefaultOptions" :> {ControllerLinking -> True}],
ImageSizeCache->{345., {290., 297.}},
SingleEvaluation->True],
Deinitialization:>None,
DynamicModuleValues:>{},
SynchronousInitialization->True,
UndoTrackedVariables:>{Typeset`show$$, 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},
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[{
$CellContext`CurvaturePlot[
Evaluate[
SetPrecision[
SetAccuracy[(1 -
Abs[((-1)^
Floor[(($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$$}], "Manipulate",
Deployed->True,
StripOnInput->False],
Manipulate`InterpretManipulate[1]]}
},
AutoDelete->False,
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
"Grid"],
TagBox[GridBox[{
{
TagBox[
StyleBox[
DynamicModuleBox[{$CellContext`\:1450\:1455$$ = 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$$}], "Manipulate",
Deployed->True,
StripOnInput->False],
Manipulate`InterpretManipulate[1]]}
},
AutoDelete->False,
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
"Grid"],
TagBox[GridBox[{
{
TagBox[
StyleBox[
DynamicModuleBox[{$CellContext`\:1450\:1455$$ = 4, $CellContext`M$$ =
1, $CellContext`\[CapitalPi]$$ =
1, $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., {215., 222.}}, 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]$$, 8}, 0, 16,
1}}, "Options" :> {FrameMargins -> 0},
"DefaultOptions" :> {ControllerLinking -> True}],
ImageSizeCache->{345., {327., 334.}},
SingleEvaluation->True],
Deinitialization:>None,
DynamicModuleValues:>{},
SynchronousInitialization->True,
UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
UnsavedVariables:>{Typeset`initDone$$},
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
Deployed->True,
StripOnInput->False],
Manipulate`InterpretManipulate[1]]}
},
AutoDelete->False,
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
"Grid"],
TagBox[GridBox[{
{
TagBox[
StyleBox[
DynamicModuleBox[{$CellContext`\:1450\:1455$$ = 8, $CellContext`M$$ =
1, $CellContext`\[CapitalPi]$$ =
1, $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., {215., 222.}}, 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]$$, 8}, 0, 16,
1}}, "Options" :> {FrameMargins -> 0},
"DefaultOptions" :> {ControllerLinking -> True}],
ImageSizeCache->{345., {327., 334.}},
SingleEvaluation->True],
Deinitialization:>None,
DynamicModuleValues:>{},
SynchronousInitialization->True,
UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
UnsavedVariables:>{Typeset`initDone$$},
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
Deployed->True,
StripOnInput->False],
Manipulate`InterpretManipulate[1]]}
},
AutoDelete->False,
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
"Grid"],
TagBox[GridBox[{
{
TagBox[
StyleBox[
DynamicModuleBox[{$CellContext`\:1450\:1455$$ = 4, $CellContext`M$$ =
0.5, $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., {77., 84.}}, 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]$$, 8}, 0, 16,
1}}, "Options" :> {FrameMargins -> 0},
"DefaultOptions" :> {ControllerLinking -> True}],
ImageSizeCache->{345., {145., 152.}},
SingleEvaluation->True],
Deinitialization:>None,
DynamicModuleValues:>{},
SynchronousInitialization->True,
UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
UnsavedVariables:>{Typeset`initDone$$},
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
Deployed->True,
StripOnInput->False],
Manipulate`InterpretManipulate[1]]}
},
AutoDelete->False,
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}],
"Grid"]}]], "Input",
CellChangeTimes->{{3.9202801568556614`*^9, 3.9202801569456615`*^9}, {
3.92028022669787*^9, 3.9202802631100445`*^9}, {3.9202803824202766`*^9,
3.920280398744342*^9}, 3.9202806958609424`*^9},
TextAlignment->Center,
CellID->116900255,ExpressionUUID->"11e490fb-ab2d-4547-86c8-ed147463c6e1"]
}, Open ]],
Cell[TextData[{
"Details",
StyleBox[" (optional) ", "SectionGloss"],
Cell[BoxData[
TemplateBox[{"Details",
Cell[
BoxData[
FrameBox[
Cell[
TextData[{
"This optional section is for a more detailed description of the \
Demonstration than the caption, but it should still be as concise as \
possible. 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. Pearson, \"A Polynomial-Time Algorithm \
for the Change-Making Problem,\" ",
StyleBox["Operations Research Letters", FontSlant -> "Italic"],
", ",
StyleBox["33", FontWeight -> "Bold"],
"(3), 2005 pp. 231\[Dash]234."}], "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->
"b42cafa3-93cc-45b2-9bce-00512b05ae14"]
}], "DetailsSection",
TextAlignment->Center,
CellTags->"Details",ExpressionUUID->"b9971572-9357-4ce2-a011-62ff9eede7fa"],
Cell[CellGroupData[{
Cell[TextData[{
"Control Suggestions",
StyleBox[" (optional) ", "SectionGloss"],
Cell[BoxData[
TemplateBox[{"Control Suggestions",
Cell[
BoxData[
FrameBox[
Cell[
TextData[{
"Check the boxes beside items that are appropriate control \
suggestions for this Demonstration. For more information, see the ",
ButtonBox[
"guidelines",
BaseStyle -> {"Hyperlink", FontColor -> RGBColor[0.4, 0.45, 0.5]},
ButtonData -> {
URL["http://demonstrations.wolfram.com/guidelines.php"], None}],
" page.",
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->
"f1fe398c-f37e-4aca-9161-633bae63965a"]
}], "ControlSuggestionsSection",
TextAlignment->Center,
CellTags->
"Control Suggestions",ExpressionUUID->"af8a4061-fdd4-44d0-82cc-\
9fec786547ab"],
Cell[BoxData[
TooltipBox[
RowBox[{
CheckboxBox[False], Cell[
" Resize Images",ExpressionUUID->"fcee1195-e255-4dbd-8863-4af840debdbd"]}],
"\"Click inside an image to reveal its orange resize frame.\\nDrag any of \
the orange resize handles to resize the image.\""]], "ControlSuggestions",
TextAlignment->Center,
FontFamily->"Verdana",
CellTags->
"ResizeImages",ExpressionUUID->"ac542041-3d26-42bf-920d-b54a74785eef"],
Cell[BoxData[
TooltipBox[
RowBox[{
CheckboxBox[False], Cell[
" Rotate and Zoom in 3D",ExpressionUUID->
"df0b52c8-7325-4803-bb1e-958545cedfd1"]}],
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.\""}]]], "ControlSuggestions",
TextAlignment->Center,
FontFamily->"Verdana",
CellTags->
"RotateAndZoomIn3D",ExpressionUUID->"e14e98ed-7514-4081-99ea-c2ffb624df9b"],
Cell[BoxData[
TooltipBox[
RowBox[{
CheckboxBox[False], Cell[
" Drag Locators",ExpressionUUID->"61b2b2a8-69c4-4012-b6da-8923112012e2"]}],
RowBox[{"\"Drag any locator (\"",
GraphicsBox[
LocatorBox[
Scaled[{0.5, 0.5}]], ImageSize -> 20],
"\", etc.) to move it around.\""}]]], "ControlSuggestions",
TextAlignment->Center,
FontFamily->"Verdana",
CellTags->
"DragLocators",ExpressionUUID->"384b79dc-c11a-492d-87e1-2c4b84403891"],
Cell[BoxData[
TooltipBox[
RowBox[{
CheckboxBox[False], Cell[
" Create and Delete Locators",ExpressionUUID->
"8e06b60e-3149-4a23-ab31-0a8ab2f5ceaf"]}],
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.\""}]]], "ControlSuggestions",
TextAlignment->Center,
FontFamily->"Verdana",
CellTags->
"CreateAndDeleteLocators",ExpressionUUID->"98a81657-e34e-4dab-ac86-\
717d7eff050a"],
Cell[BoxData[
TooltipBox[
RowBox[{
CheckboxBox[False], Cell[
" Slider Zoom",ExpressionUUID->"c8d377e3-56fc-4adc-88e3-cf7642fb3181"]}],
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.\""}]]], "ControlSuggestions",
TextAlignment->Center,
FontFamily->"Verdana",
CellTags->
"SliderZoom",ExpressionUUID->"b84ac2ce-e422-4d4d-953e-073d63c15a9e"],
Cell[BoxData[
TooltipBox[
RowBox[{
CheckboxBox[False], Cell[
" Gamepad Controls",ExpressionUUID->
"1fbb5ded-9a1c-4ba0-a087-0d1c0be219ce"]}],
"\"Control this Demonstration with a gamepad or other\\nhuman interface \
device connected to your computer.\""]], "ControlSuggestions",
CellChangeTimes->{3.35696210375764*^9, 3.3895522232313623`*^9},
TextAlignment->Center,
FontFamily->"Verdana",
CellTags->
"GamepadControls",ExpressionUUID->"b4dbde82-29d9-4853-88cd-e053ae8d181c"],
Cell[BoxData[
TooltipBox[
RowBox[{
CheckboxBox[False], Cell[
" Automatic Animation",ExpressionUUID->
"ec8a5240-77b9-42a0-8b9e-365efb47dfeb"]}],
RowBox[{"\"Animate a slider in this Demonstration by clicking the\"",
AdjustmentBox[
Cell[
GraphicsData[
"CompressedBitmap",
"eJzzTSzJSM1NLMlMTlRwL0osyMhMLlZwyy8CCjEzMjAwcIKwAgOI/R/IhBKc\n\
/4EAyGAG0f+nTZsGwgysIJIRKsWKLAXGIHFmEpUgLADxWUAkI24jZs+eTaEt\n\
IG+wQKRmzJgBlYf5lhEA30OqWA=="], "Graphics", ImageSize -> {9, 9}, ImageMargins ->
0, CellBaseline -> Baseline], BoxBaselineShift -> 0.1839080459770115,
BoxMargins -> {{0., 0.}, {-0.1839080459770115, 0.1839080459770115}}],
"\"button\\nnext to the slider, and then clicking the play button that \
appears.\\nAnimate all controls by selecting \"",
StyleBox["Autorun", FontWeight -> "Bold"], "\" from the\"",
AdjustmentBox[
Cell[
GraphicsData[
"CompressedBitmap",
"eJyNULENwyAQfEySIlMwTVJlCGRFsosokeNtqBmDBagoaZjAI1C8/8GUUUC6\n\
57h7cQ8PvU7Pl17nUav7oj/TPH7V7b2QJAUAXBkKmCPRowxICy64bRvGGNF7\n\
X8CctGoDSN4xhIDGGDhzFXwUh3/ClBKrDQPmnGXtI6u0OOd+tZBVUqy1xSaH\n\
UqiK6pPe4XdEdAz6563tx/gejuORGMxJaz8mdpJn7hc="], "Graphics",
ImageSize -> {10, 10}, ImageMargins -> 0, CellBaseline -> Baseline],
BoxBaselineShift -> 0.1839080459770115,
BoxMargins -> {{0., 0.}, {-0.1839080459770115, 0.1839080459770115}}],
"\"menu.\""}]]], "ControlSuggestions",
TextAlignment->Center,
FontFamily->"Verdana",
CellTags->
"AutomaticAnimation",ExpressionUUID->"6e84bbe0-7d8e-44ab-aac1-048973c18d4f"],
Cell[BoxData[
TooltipBox[
RowBox[{
CheckboxBox[False], Cell[
" Bookmark Animation",ExpressionUUID->
"5bdb2812-7da3-4bb1-a7fc-436054c40542"]}],
RowBox[{
"\"See a prepared animation of this Demonstration by selecting\\n\"",
StyleBox["Animate Bookmarks", FontWeight -> "Bold"], "\" from the\"",
AdjustmentBox[
Cell[
GraphicsData[
"CompressedBitmap",
"eJyNULENwyAQfEySIlMwTVJlCGRFsosokeNtqBmDBagoaZjAI1C8/8GUUUC6\n\
57h7cQ8PvU7Pl17nUav7oj/TPH7V7b2QJAUAXBkKmCPRowxICy64bRvGGNF7\n\
X8CctGoDSN4xhIDGGDhzFXwUh3/ClBKrDQPmnGXtI6u0OOd+tZBVUqy1xSaH\n\
UqiK6pPe4XdEdAz6563tx/gejuORGMxJaz8mdpJn7hc="], "Graphics",
ImageSize -> {10, 10}, ImageMargins -> 0, CellBaseline -> Baseline],
BoxBaselineShift -> 0.1839080459770115,
BoxMargins -> {{0., 0.}, {-0.1839080459770115, 0.1839080459770115}}],
"\"menu.\""}]]], "ControlSuggestions",
TextAlignment->Center,
FontFamily->"Verdana",
CellTags->
"BookmarkAnimation",ExpressionUUID->"0cf5a50d-6c0e-4089-a29f-941bc4ca8891"]
}, Open ]],
Cell[TextData[{
"Search Terms",
StyleBox[" (optional) ", "SectionGloss"],
Cell[BoxData[
TemplateBox[{"Search Terms",
Cell[
BoxData[
FrameBox[
Cell[
TextData[{
"Provide words and phrases that people might search for, with each \
one in a separate cell. 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. Do not \
capitalize words unless they are proper names or proper adjectives.",
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->
"b8b4550c-a7c1-4c5e-acf4-64f68ac8ea51"]
}], "SearchTermsSection",
TextAlignment->Center,
CellTags->
"Search Terms",ExpressionUUID->"a3a3a6a7-7876-4115-a51a-6d092bee139b"],
Cell[TextData[{
"Related Links",
StyleBox[" (optional) ", "SectionGloss"],
Cell[BoxData[
TemplateBox[{"Related Links",
Cell[
BoxData[
FrameBox[
Cell[
TextData[{
"Provide hyperlinks (not just bare URLs) to any relevant wolfram.com \
pages, with the page title as the linked text. Links to ",
ButtonBox[
"NKS | Online",
BaseStyle -> {"Hyperlink", FontColor -> RGBColor[0.4, 0.45, 0.5]},
ButtonData -> {
URL["http://www.wolframscience.com/nks"], None}],
" should use the section title, not a page number. Links to \
non-Wolfram sites go 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->
"d5b26c0d-c135-41cd-9d97-dc9003b05c57"]
}], "RelatedLinksSection",
TextAlignment->Center,
CellTags->
"Related Links",ExpressionUUID->"83b0243b-b7e3-4afb-8a4e-185fec8161fe"],
Cell[CellGroupData[{
Cell[TextData[{
"Authoring Information",
Cell[BoxData[
TemplateBox[{"Authoring Information",
Cell[
BoxData[
FrameBox[
Cell[
TextData[{
"'Contributed by: John Smith' for single authors; 'Contributed by: \
John Smith, Robert Ford, and Jane Doe' for multiple authors. To credit people \
other than Demonstrations authors, please see the detailed ",
ButtonBox[
"guidelines",
BaseStyle -> {"Hyperlink", FontColor -> RGBColor[0.4, 0.45, 0.5]},
ButtonData -> {
URL["http://demonstrations.wolfram.com/guidelines.php"], None}],
".",
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->
"990970f3-a922-4bea-919a-d6fa2da1f6d5"]
}], "AuthorSection",
TextAlignment->Center,
CellTags->
"Authoring \
Information",ExpressionUUID->"c2736cdb-c24c-4dd4-9a22-5bbef1a7a20a"],
Cell["", "Author",
CellChangeTimes->{
3.35696210375764*^9, {3.432333043774981*^9, 3.432333045441087*^9},
3.920280830122656*^9},
TextAlignment->Center,ExpressionUUID->"e6a077c9-f528-4852-97e7-764f2f3a1895"]
}, Open ]]
}, Open ]]
},
ScreenStyleEnvironment->"DemonstrationSource",
WindowSize->{700, 848},
WindowMargins->{{486, Automatic}, {Automatic, 64}},
TaggingRules->{
"DocuToolsSettingsInternal" -> {
"$PacletVersion" -> "0.10.2121", "$MVersion" -> "12", "$FlaggedVersion" ->
11.3, "$ApplicationName" -> "Pubs", "$LinkBase" -> "Pubs",
"$ApplicationDirectory" -> "C:\\Users\\jayw\\Desktop\\CVSTree\\Pubs\\",
"$DocumentationDirectory" ->
"C:\\Users\\jayw\\Desktop\\CVSTree\\Pubs\\Documentation\\English\\",
"$UseNewPageDialog" -> "False", "$CondensedBlogMenus" -> "True"},
"PresenterSettings" -> {
"OutlineThumbnails" -> {"1" -> "Thumbnail"},
"OutlinePalette" -> {"Thumbnails" -> {}, "ThumbnailMagnification" -> 0.8},
"SideNotesPalette" -> {"PaletteNumber" -> 0}}, "BlogsDirectory" ->
"\\\\wrisync02.wri.wolfram.com\\backup$\\jayw\\My \
Documents\\jaywstasks\\BlogTools\\Blogs\\", "ChatNotebookID" ->
"fef9786d-4748-42a0-a328-5496e837f205", "Originator" ->
"chatframework@wolfram.com", "ScreenName" -> "", "ChatCreationDate" ->
"DateObject[{2018, 6, 18, 13, 5, 54.5673134}, Instant, Gregorian, -5.]",
"CustomWindowTitle" -> "None", "ChatNotebookDate" -> "18 Jun 2018 13:05:54",
"ChatNotebookWindowTitle" -> "chatframework's Chat - (18 Jun 2018 13:05)",
"Participants" -> {"chatframework@wolfram.com", "wan4ren2jie2@gmail.com"},
"AllParticipants" -> {
"chatframework@wolfram.com", "wan4ren2jie2@gmail.com"},
"Contacts" -> {
"andre@wolfram.com", "bradym@wolfram.com", "brianv@wolfram.com",
"jayw@wolfram.com", "wan4ren2jie2@gmail.com"},
"EmailListData" -> {0, 0, 0, 0, 1}, "ScrollLock" -> False, "Terminated" ->
True, "QuestionState" -> "Timeup",
"AttachedCells" -> {
"Initialization Code" -> None, "Manipulate" -> None, "Caption" -> None,
"Snapshots" -> None, "Details" -> None, "Related Links" -> None,
"Search Terms" -> None, "Control Suggestions" -> None, "Thumbnail" ->
None, "Authoring Information" -> CellObject[1160241]}},
FrontEndVersion->"12.2 for Microsoft Windows (64-bit) (December 12, 2020)",
StyleDefinitions->Notebook[{
Cell[
StyleData[
StyleDefinitions ->
FrontEnd`FileName[{"Wolfram"}, "Demonstration.nb", CharacterEncoding ->
"UTF-8"]], TextAlignment -> Center],
Cell[
StyleData[All], TextAlignment -> Center]}, WindowSize -> {785, 884},
WindowMargins -> {{190, Automatic}, {0, Automatic}}, Visible -> False,
FrontEndVersion ->
"12.2 for Microsoft Windows (64-bit) (December 12, 2020)", StyleDefinitions ->
"PrivateStylesheetFormatting.nb"],
ExpressionUUID->"8df33655-38cd-478b-94a3-0ff3a7d16b08"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
"Authoring Information"->{
Cell[72685, 1728, 1182, 29, 156, "AuthorSection",ExpressionUUID->"c2736cdb-c24c-4dd4-9a22-5bbef1a7a20a",
CellTags->"Authoring Information"]},
"AutomaticAnimation"->{
Cell[67707, 1605, 1588, 34, 22, "ControlSuggestions",ExpressionUUID->"6e84bbe0-7d8e-44ab-aac1-048973c18d4f",
CellTags->"AutomaticAnimation"]},
"BookmarkAnimation"->{
Cell[69298, 1641, 1032, 24, 22, "ControlSuggestions",ExpressionUUID->"0cf5a50d-6c0e-4089-a29f-941bc4ca8891",
CellTags->"BookmarkAnimation"]},
"Caption"->{
Cell[31698, 812, 1162, 25, 67, "ManipulateCaptionSection",ExpressionUUID->"3ed78bfd-4459-4d2a-906f-3e9e6aba33a4",
CellTags->"Caption"]},
"Control Suggestions"->{
Cell[62610, 1464, 1155, 29, 67, "ControlSuggestionsSection",ExpressionUUID->"af8a4061-fdd4-44d0-82cc-9fec786547ab",
CellTags->"Control Suggestions"]},
"CreateAndDeleteLocators"->{
Cell[65474, 1544, 763, 19, 22, "ControlSuggestions",ExpressionUUID->"98a81657-e34e-4dab-ac86-717d7eff050a",
CellTags->"CreateAndDeleteLocators"]},
"Details"->{
Cell[60765, 1423, 1820, 37, 67, "DetailsSection",ExpressionUUID->"b9971572-9357-4ce2-a011-62ff9eede7fa",
CellTags->"Details"]},
"DragLocators"->{
Cell[65012, 1529, 459, 13, 22, "ControlSuggestions",ExpressionUUID->"384b79dc-c11a-492d-87e1-2c4b84403891",
CellTags->"DragLocators"]},
"GamepadControls"->{
Cell[67211, 1591, 493, 12, 22, "ControlSuggestions",ExpressionUUID->"b4dbde82-29d9-4853-88cd-e053ae8d181c",
CellTags->"GamepadControls"]},
"Initialization Code"->{
Cell[2048, 48, 1857, 40, 67, "InitializationSection",ExpressionUUID->"1d34a731-8c48-4189-8b6f-89ef5777db9f",
CellTags->"Initialization Code"]},
"Manipulate"->{
Cell[19310, 516, 1548, 31, 67, "ManipulateSection",ExpressionUUID->"b7acceb9-ca4b-4965-b319-bd8a6214a587",
CellTags->"Manipulate"]},
"Related Links"->{
Cell[71445, 1695, 1215, 29, 67, "RelatedLinksSection",ExpressionUUID->"83b0243b-b7e3-4afb-8a4e-185fec8161fe",
CellTags->"Related Links"]},
"ResizeImages"->{
Cell[63768, 1495, 431, 10, 22, "ControlSuggestions",ExpressionUUID->"ac542041-3d26-42bf-920d-b54a74785eef",
CellTags->"ResizeImages"]},
"RotateAndZoomIn3D"->{
Cell[64202, 1507, 807, 20, 22, "ControlSuggestions",ExpressionUUID->"e14e98ed-7514-4081-99ea-c2ffb624df9b",
CellTags->"RotateAndZoomIn3D"]},
"Search Terms"->{
Cell[70345, 1668, 1097, 25, 67, "SearchTermsSection",ExpressionUUID->"a3a3a6a7-7876-4115-a51a-6d092bee139b",
CellTags->"Search Terms"]},
"SliderZoom"->{
Cell[66240, 1565, 968, 24, 22, "ControlSuggestions",ExpressionUUID->"b84ac2ce-e422-4d4d-953e-073d63c15a9e",
CellTags->"SliderZoom"]},
"Snapshots"->{
Cell[38448, 964, 1042, 23, 67, "SnapshotsSection",ExpressionUUID->"96bb7a68-4496-4362-86d3-c2a0812907f2",
CellTags->"Snapshots"]},
"Thumbnail"->{
Cell[33078, 846, 1029, 23, 67, "ThumbnailSection",ExpressionUUID->"401cc3c4-8319-4e19-82e7-df5fcb711a42",
CellTags->"Thumbnail"]}
}
*)
(*CellTagsIndex
CellTagsIndex->{
{"Authoring Information", 76876, 1822},
{"AutomaticAnimation", 77048, 1825},
{"BookmarkAnimation", 77220, 1828},
{"Caption", 77381, 1831},
{"Control Suggestions", 77549, 1834},
{"CreateAndDeleteLocators", 77735, 1837},
{"Details", 77901, 1840},
{"DragLocators", 78053, 1843},
{"GamepadControls", 78216, 1846},
{"Initialization Code", 78386, 1849},
{"Manipulate", 78552, 1852},
{"Related Links", 78710, 1855},
{"ResizeImages", 78873, 1858},
{"RotateAndZoomIn3D", 79038, 1861},
{"Search Terms", 79203, 1864},
{"SliderZoom", 79362, 1867},
{"Snapshots", 79517, 1870},
{"Thumbnail", 79669, 1873}
}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 1443, 22, 90, "Title",ExpressionUUID->"b9e6fe14-67c5-4f7d-9ec0-13c361826e91"],
Cell[CellGroupData[{
Cell[2048, 48, 1857, 40, 67, "InitializationSection",ExpressionUUID->"1d34a731-8c48-4189-8b6f-89ef5777db9f",
CellTags->"Initialization Code"],
Cell[3908, 90, 5880, 163, 418, "Input",ExpressionUUID->"ee244b7a-a530-47db-8602-9dbd7bcdc504",
CellID->24701595],
Cell[9791, 255, 6595, 179, 454, "Input",ExpressionUUID->"c1a65306-27f7-4756-940f-772f9967450d",
CellID->25712845],
Cell[16389, 436, 2884, 75, 76, "Input",ExpressionUUID->"8d88b28f-3f47-427b-b865-62c1837375dc",
CellID->77166300]
}, Open ]],
Cell[CellGroupData[{
Cell[19310, 516, 1548, 31, 67, "ManipulateSection",ExpressionUUID->"b7acceb9-ca4b-4965-b319-bd8a6214a587",
CellTags->"Manipulate"],
Cell[CellGroupData[{
Cell[20883, 551, 6395, 163, 112, "Input",ExpressionUUID->"1c8a51fe-61b3-446f-b3f3-b27c622b6763"],
Cell[27281, 716, 4368, 90, 599, "Output",ExpressionUUID->"dfd01e67-d611-4c3e-aa0e-2487522ca13a",
CellID->397291535]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[31698, 812, 1162, 25, 67, "ManipulateCaptionSection",ExpressionUUID->"3ed78bfd-4459-4d2a-906f-3e9e6aba33a4",
CellTags->"Caption"],
Cell[32863, 839, 178, 2, 22, "ManipulateCaption",ExpressionUUID->"71921e4e-c8c2-4f05-96e3-4e3047349e9a"]
}, Open ]],
Cell[CellGroupData[{
Cell[33078, 846, 1029, 23, 67, "ThumbnailSection",ExpressionUUID->"401cc3c4-8319-4e19-82e7-df5fcb711a42",
CellTags->"Thumbnail"],
Cell[34110, 871, 4301, 88, 687, "Output",ExpressionUUID->"1b37c0f7-f862-4bde-95eb-3c9910bdd789",
CellID->63458145]
}, Open ]],
Cell[CellGroupData[{
Cell[38448, 964, 1042, 23, 67, "SnapshotsSection",ExpressionUUID->"96bb7a68-4496-4362-86d3-c2a0812907f2",
CellTags->"Snapshots"],
Cell[39493, 989, 21257, 431, 3094, InheritFromParent,ExpressionUUID->"11e490fb-ab2d-4547-86c8-ed147463c6e1",
CellID->116900255]
}, Open ]],
Cell[60765, 1423, 1820, 37, 67, "DetailsSection",ExpressionUUID->"b9971572-9357-4ce2-a011-62ff9eede7fa",
CellTags->"Details"],
Cell[CellGroupData[{
Cell[62610, 1464, 1155, 29, 67, "ControlSuggestionsSection",ExpressionUUID->"af8a4061-fdd4-44d0-82cc-9fec786547ab",
CellTags->"Control Suggestions"],
Cell[63768, 1495, 431, 10, 22, "ControlSuggestions",ExpressionUUID->"ac542041-3d26-42bf-920d-b54a74785eef",
CellTags->"ResizeImages"],
Cell[64202, 1507, 807, 20, 22, "ControlSuggestions",ExpressionUUID->"e14e98ed-7514-4081-99ea-c2ffb624df9b",
CellTags->"RotateAndZoomIn3D"],
Cell[65012, 1529, 459, 13, 22, "ControlSuggestions",ExpressionUUID->"384b79dc-c11a-492d-87e1-2c4b84403891",
CellTags->"DragLocators"],
Cell[65474, 1544, 763, 19, 22, "ControlSuggestions",ExpressionUUID->"98a81657-e34e-4dab-ac86-717d7eff050a",
CellTags->"CreateAndDeleteLocators"],
Cell[66240, 1565, 968, 24, 22, "ControlSuggestions",ExpressionUUID->"b84ac2ce-e422-4d4d-953e-073d63c15a9e",
CellTags->"SliderZoom"],
Cell[67211, 1591, 493, 12, 22, "ControlSuggestions",ExpressionUUID->"b4dbde82-29d9-4853-88cd-e053ae8d181c",
CellTags->"GamepadControls"],
Cell[67707, 1605, 1588, 34, 22, "ControlSuggestions",ExpressionUUID->"6e84bbe0-7d8e-44ab-aac1-048973c18d4f",
CellTags->"AutomaticAnimation"],
Cell[69298, 1641, 1032, 24, 22, "ControlSuggestions",ExpressionUUID->"0cf5a50d-6c0e-4089-a29f-941bc4ca8891",
CellTags->"BookmarkAnimation"]
}, Open ]],
Cell[70345, 1668, 1097, 25, 67, "SearchTermsSection",ExpressionUUID->"a3a3a6a7-7876-4115-a51a-6d092bee139b",
CellTags->"Search Terms"],
Cell[71445, 1695, 1215, 29, 67, "RelatedLinksSection",ExpressionUUID->"83b0243b-b7e3-4afb-8a4e-185fec8161fe",
CellTags->"Related Links"],
Cell[CellGroupData[{
Cell[72685, 1728, 1182, 29, 156, "AuthorSection",ExpressionUUID->"c2736cdb-c24c-4dd4-9a22-5bbef1a7a20a",
CellTags->"Authoring Information"],
Cell[73870, 1759, 213, 4, 22, "Author",ExpressionUUID->"e6a077c9-f528-4852-97e7-764f2f3a1895"]
}, Open ]]
}, Open ]]
}
]
*)