O-/𖣠⚪∣❁∣✤✻ЭЄᗩߦറ⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪റߦᗩЭЄ✻✤∣❁∣⚪𖣠/𖣠⚪ИNⓄꖴ✤ᑐᑕИNᑎꗳ𖣓ᔓᔕᑎꖴ⚭ᗩꗳ⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪ꗳᗩ⚭ꖴᑎᔓᔕ𖣓ꗳᑎИNᑐᑕ✤ꖴⓄИN⚪𖣠/𖣠⚪ᗱᗴᴥᑎ✤ᗩᗯᴥᑎᑐᑕ⚪𖡼𖡼𖡼𖡼⚪𔗢⚪🞋⚪𔗢⚪𖡼𖡼𖡼𖡼⚪ᑐᑕᑎᴥᗯᗩ✤ᑎᴥᗱᗴ⚪𖣠/ᗺИ.𖣠⚪ИNⓄꖴ✤ᗩᙁᑎߦꖴИNᗩᙏ⚙ᔓᔕᴥᗱᗴИNᴥⓄᑐᑕ𖣓ᗱᗴᙁ⚭ᗩꖴᴥᗩᗯ᳀ᔓᔕᑎꖴ⚭ᗩꗳ⚪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⚪ꗳᗩ⚭ꖴᑎᔓᔕ᳀ᗯᗩᴥꖴᗩ⚭ᙁᗱᗴ𖣓ᑐᑕⓄᴥИNᗱᗴᴥᔓᔕ⚙ᙏᗩИNꖴߦᑎᙁᗩ✤ꖴⓄИN⚪𖣠.NB
2024-04-05 12:09:12 +00:00

730 lines
29 KiB
Mathematica

(* 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[ 28894, 721]
NotebookOptionsPosition[ 27728, 692]
NotebookOutlinePosition[ 28613, 718]
CellTagsIndexPosition[ 28570, 715]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
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"}], "}"}], ",", "\n", " ",
RowBox[{
RowBox[{"sol", " ", "=", " ",
RowBox[{"NDSolve", "[",
RowBox[{
RowBox[{"{", "\n", " ",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"\[Theta]", "'"}], "[", "t", "]"}], " ", "==", " ", "f"}],
",", "\n", " ",
RowBox[{
RowBox[{
RowBox[{"x", "'"}], "[", "t", "]"}], " ", "==", " ",
RowBox[{"Cos", "[",
RowBox[{"\[Theta]", "[", "t", "]"}], "]"}]}], ",", "\n", " ",
RowBox[{
RowBox[{
RowBox[{"y", "'"}], "[", "t", "]"}], " ", "==", " ",
RowBox[{"Sin", "[",
RowBox[{"\[Theta]", "[", "t", "]"}], "]"}]}], ",", "\n", " ",
RowBox[{
RowBox[{"\[Theta]", "[", "tmin", "]"}], " ", "==", " ",
"\[Theta]0"}], ",", "\n", " ",
RowBox[{
RowBox[{"x", "[", "tmin", "]"}], " ", "==", " ", "x0"}], ",", "\n",
" ",
RowBox[{
RowBox[{"y", "[", "tmin", "]"}], " ", "==", " ", "y0"}]}], "\n",
" ", "}"}], ",", " ",
RowBox[{"{",
RowBox[{"x", ",", " ", "y"}], "}"}], ",", " ",
RowBox[{"{",
RowBox[{"t", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",", " ",
"opts"}], "]"}]}], ";", "\n", " ",
RowBox[{"if", " ", "=", " ",
RowBox[{
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"x", "[", "#", "]"}], ",", " ",
RowBox[{"y", "[", "#", "]"}]}], "}"}], " ", "&"}], " ", "/.", " ",
RowBox[{"First", "[", "sol", "]"}]}]}], ";", "\n", " ", "if"}]}],
"\n", " ", "]"}]}], "\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"}],
"}"}], ",", "\n", " ",
RowBox[{
RowBox[{"rlsplot", " ", "=", " ",
RowBox[{"FilterRules", "[",
RowBox[{
RowBox[{"{", "opts", "}"}], ",", " ",
RowBox[{"Options", "[", "ParametricPlot", "]"}]}], "]"}]}], ";", "\n",
" ",
RowBox[{"rlsndsolve", " ", "=", " ",
RowBox[{"FilterRules", "[",
RowBox[{
RowBox[{"{", "opts", "}"}], ",", " ",
RowBox[{"Options", "[", "NDSolve", "]"}]}], "]"}]}], ";", "\n", " ",
RowBox[{"If", "[",
RowBox[{
RowBox[{
RowBox[{"Head", "[", "f", "]"}], " ", "===", " ", "List"}], ",", "\n",
" ",
RowBox[{
RowBox[{"ifs", " ", "=", " ",
RowBox[{
RowBox[{
RowBox[{"iCurvaturePlotHelper", "[",
RowBox[{"#", ",", " ",
RowBox[{"{",
RowBox[{"t", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",",
" ", "p", ",", " ",
RowBox[{"Evaluate", "@",
RowBox[{"(",
RowBox[{"Sequence", " ", "@@", " ", "rlsndsolve"}], ")"}]}]}],
"]"}], " ", "&"}], " ", "/@", " ", "f"}]}], ";", "\n", " ",
RowBox[{"ParametricPlot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{
RowBox[{
RowBox[{"#", "[", "tplot", "]"}], " ", "&"}], " ", "/@", " ",
"ifs"}], "]"}], ",", " ",
RowBox[{"{",
RowBox[{"tplot", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",",
" ",
RowBox[{"Evaluate", "@",
RowBox[{"(",
RowBox[{"Sequence", " ", "@@", " ", "rlsplot"}], ")"}]}]}],
"]"}]}], "\n", " ", ",", "\n", " ",
RowBox[{
RowBox[{"if", " ", "=", " ",
RowBox[{"iCurvaturePlotHelper", "[",
RowBox[{"f", ",", " ",
RowBox[{"{",
RowBox[{"t", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",",
" ", "p", ",", " ",
RowBox[{"Evaluate", "@",
RowBox[{"(",
RowBox[{"Sequence", " ", "@@", " ", "rlsndsolve"}], ")"}]}]}],
"]"}]}], ";", "\n", " ",
RowBox[{"ParametricPlot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{"if", "[", "tplot", "]"}], "]"}], ",", " ",
RowBox[{"{",
RowBox[{"tplot", ",", " ", "tmin", ",", " ", "tmax"}], "}"}], ",",
" ",
RowBox[{"Evaluate", "@",
RowBox[{"(",
RowBox[{"Sequence", " ", "@@", " ", "rlsplot"}], ")"}]}]}],
"]"}]}]}], "\n", " ", "]"}]}]}], "\n", " ", "]"}]}]}], "Input",
TextAlignment->Center,
FontFamily->"Go Noto Current-Regular",
FontSize->10,
FontWeight->"Normal",
CellLabel->
"4/3/24 21:38:11 \
In[5275]:=",ExpressionUUID->"670c0d5c-4772-49bb-b74f-ae6a69be9ed0"],
Cell[BoxData[
RowBox[{"\[IndentingNewLine]",
RowBox[{
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",
FontFamily->"Go Noto Current-Regular",
FontSize->10,
FontWeight->"Normal",
CellLabel->
"4/3/24 21:38:11 \
In[5279]:=",ExpressionUUID->"a4addeb7-2708-41df-8367-f56fd1c4c60d"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"\:15e9", "=", "90"}], ";",
RowBox[{"\:042fR", "=",
RowBox[{"(",
RowBox[{"4", "/", "8"}], ")"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"Grid", "[",
RowBox[{"{",
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{"Manipulate", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"\:1513\:1515", "=",
RowBox[{"{",
RowBox[{
RowBox[{"WorkingPrecision", "\[Rule]", "\:041fW\:041f"}], ",",
RowBox[{"ImageSize", "\[Rule]", "256"}], ",",
RowBox[{"Axes", "\[Rule]", "True"}], ",",
RowBox[{"MaxRecursion", "\[Rule]", "0"}], ",",
RowBox[{"PlotPoints", "\[Rule]",
RowBox[{"1", "+",
SuperscriptBox["2", "\[CapitalPi]\[CapitalPi]"]}]}], ",",
RowBox[{"PlotStyle", "\[Rule]",
RowBox[{"Thickness", "[", "0.00001", "]"}]}], ",",
RowBox[{"PlotLegends", "\[Rule]", " ",
RowBox[{"Placed", "[",
RowBox[{"\"\<Expressions\>\"", ",",
RowBox[{"{",
RowBox[{"Center", ",", "Top"}], "}"}]}], "]"}]}], ",",
RowBox[{"PlotRangePadding", "\[Rule]",
RowBox[{"4", "/", "256"}]}], ",",
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"}], "]"}]}]}], "}"}]}], ";",
"\[IndentingNewLine]",
RowBox[{"\:1586\:1587", "=",
RowBox[{"{",
RowBox[{"x", ",", "0", ",",
RowBox[{
RowBox[{
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi"}]}], "}"}]}],
";", "\[IndentingNewLine]",
RowBox[{"\:a5f3", "=",
RowBox[{"Piecewise", "[",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{"FabiusF", "[",
RowBox[{
RowBox[{
RowBox[{"x", "/", "\:042fR"}], "/", "Pi"}],
RowBox[{
RowBox[{"(",
RowBox[{"360", "/", "\:15e9"}], ")"}], "/", "4"}]}], "]"}],
"]"}], ",",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi", "*",
"\:042fR", "*", "0"}], "<", "x", "<",
RowBox[{
RowBox[{
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi", "*",
"\:042fR"}]}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"Abs", "[",
RowBox[{"FabiusF", "[",
RowBox[{"1", "-",
RowBox[{"(",
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"x", "/", "Pi"}],
RowBox[{
RowBox[{"(",
RowBox[{"360", "/", "\:15e9"}], ")"}], "/", "4"}]}],
")"}], "-", "\:042fR"}], ")"}], "/",
RowBox[{"(",
RowBox[{"1", "-", "\:042fR"}], ")"}]}], ")"}], ")"}]}],
"]"}], "]"}], ",",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi", "*",
"\:042fR"}], "<", "x", "<",
RowBox[{
RowBox[{
RowBox[{"(", "\:15e9", ")"}], "/", "90"}], "*", "Pi", "*",
"1"}]}]}], "}"}]}], "}"}], "]"}]}], ";", "\[IndentingNewLine]",
RowBox[{"Column", "[",
RowBox[{"{",
RowBox[{
RowBox[{"CurvaturePlot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{"SetPrecision", "[",
RowBox[{
RowBox[{"SetAccuracy", "[",
RowBox[{"\:a5f3", ",", "\:041fW\:041f"}], "]"}], ",",
"\:041fW\:041f"}], "]"}], "]"}], ",",
RowBox[{"Evaluate", "[", "\:1586\:1587", "]"}], ",",
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[{"Plot", "[",
RowBox[{
RowBox[{"Evaluate", "[",
RowBox[{"SetPrecision", "[",
RowBox[{
RowBox[{"SetAccuracy", "[",
RowBox[{"\:a5f3", ",", "\:041fW\:041f"}], "]"}], ",",
"\:041fW\:041f"}], "]"}], "]"}], ",",
RowBox[{"Evaluate", "[", "\:1586\:1587", "]"}], ",",
RowBox[{"Evaluate", "[", "\:1513\:1515", "]"}], ",",
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"}]}], "]"}]}], "}"}]}]}], " ", "]"}]}],
"}"}], "]"}]}], "\[IndentingNewLine]", ",", "\[IndentingNewLine]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\:15e9", ",", "90"}], "}"}], ",", "0", ",", "360", ",",
RowBox[{"1", "/", "256"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\:042fR", ",",
RowBox[{"4", "/", "8"}], ",", "\"\<\[CenterDot]|\[CenterDot]\>\""}],
"}"}], ",", "0", ",", "1", ",",
RowBox[{"1", "/", "256"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\[CapitalPi]\[CapitalPi]", ",", "8"}], "}"}], ",", "0", ",",
"16", ",", "1"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"\:041fW\:041f", ",", "16"}], "}"}], ",", "0", ",", "64",
",", "1"}], "}"}], "\[IndentingNewLine]", ",",
RowBox[{"FrameMargins", "\[Rule]", "0"}]}], "\[IndentingNewLine]",
"]"}], "\[IndentingNewLine]", "}"}], "}"}], "]"}]}], "Input",
FontFamily->"Go Noto Current-Regular",
FontSize->10,
FontWeight->"Normal",ExpressionUUID->"adf5a779-403a-4c2b-985b-3306f9c44e28"],
Cell[BoxData[
TagBox[GridBox[{
{
TagBox[
StyleBox[
DynamicModuleBox[{XMPTools`Wrappers`Private`\:15e9$$ = 90,
XMPTools`Wrappers`Private`\:042fR$$ = Rational[1, 2],
XMPTools`Wrappers`Private`\:041fW\:041f$$ = 16,
XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$ = 8,
Typeset`show$$ = True, Typeset`bookmarkList$$ = {},
Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$,
Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"",
Typeset`specs$$ = {{{
Hold[XMPTools`Wrappers`Private`\:15e9$$], 90}, 0, 360,
Rational[1, 256]}, {{
Hold[XMPTools`Wrappers`Private`\:042fR$$],
Rational[1, 2], "\[CenterDot]|\[CenterDot]"}, 0, 1,
Rational[1, 256]}, {{
Hold[XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$], 8}, 0,
16, 1}, {{
Hold[XMPTools`Wrappers`Private`\:041fW\:041f$$], 16}, 0, 64, 1}},
Typeset`size$$ = {256., {242., 247.}}, Typeset`update$$ = 0,
Typeset`initDone$$, Typeset`skipInitDone$$ = True},
DynamicBox[Manipulate`ManipulateBoxes[
1, StandardForm,
"Variables" :> {
XMPTools`Wrappers`Private`\:15e9$$ = 90,
XMPTools`Wrappers`Private`\:042fR$$ = Rational[1, 2],
XMPTools`Wrappers`Private`\:041fW\:041f$$ = 16,
XMPTools`Wrappers`Private`\[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" :> (
XMPTools`Wrappers`Private`\:1513\:1515 = {
WorkingPrecision -> XMPTools`Wrappers`Private`\:041fW\:041f$$,
ImageSize -> 256, Axes -> True, MaxRecursion -> 0, PlotPoints ->
1 + 2^XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$,
PlotStyle -> Thickness[0.00001], PlotLegends ->
Placed["Expressions", {Center, Top}], PlotRangePadding -> 4/256,
PlotRange -> Full, Frame -> True, Axes -> False,
GridLines -> {{0}, {0}}, PlotStyle -> GrayLevel[168/256],
FrameStyle -> GrayLevel[178/256]};
XMPTools`Wrappers`Private`\:1586\:1587 = {
XMPTools`Wrappers`Private`x,
0, (XMPTools`Wrappers`Private`\:15e9$$/90) Pi};
XMPTools`Wrappers`Private`\:a5f3 = Piecewise[{{
Abs[
XMPTools`Wrappers`Private`FabiusF[((
XMPTools`Wrappers`Private`x/
XMPTools`Wrappers`Private`\:042fR$$)/
Pi) ((360/XMPTools`Wrappers`Private`\:15e9$$)/
4)]], (((XMPTools`Wrappers`Private`\:15e9$$/90) Pi)
XMPTools`Wrappers`Private`\:042fR$$) 0 <
XMPTools`Wrappers`Private`x < ((
XMPTools`Wrappers`Private`\:15e9$$/90) Pi)
XMPTools`Wrappers`Private`\:042fR$$}, {
Abs[
XMPTools`Wrappers`Private`FabiusF[
1 - ((XMPTools`Wrappers`Private`x/
Pi) ((360/XMPTools`Wrappers`Private`\:15e9$$)/4) -
XMPTools`Wrappers`Private`\:042fR$$)/(1 -
XMPTools`Wrappers`Private`\:042fR$$)]], ((
XMPTools`Wrappers`Private`\:15e9$$/90) Pi)
XMPTools`Wrappers`Private`\:042fR$$ <
XMPTools`Wrappers`Private`x < ((
XMPTools`Wrappers`Private`\:15e9$$/90) Pi) 1}}]; Column[{
XMPTools`Wrappers`Private`CurvaturePlot[
Evaluate[
SetPrecision[
SetAccuracy[
XMPTools`Wrappers`Private`\:a5f3,
XMPTools`Wrappers`Private`\:041fW\:041f$$],
XMPTools`Wrappers`Private`\:041fW\:041f$$]],
Evaluate[XMPTools`Wrappers`Private`\:1586\:1587],
Evaluate[XMPTools`Wrappers`Private`\:1513\:1515], FrameTicks -> {
Range[-16, 16, 1/2],
Range[-4, 4, 1/2]}],
Plot[
Evaluate[
SetPrecision[
SetAccuracy[
XMPTools`Wrappers`Private`\:a5f3,
XMPTools`Wrappers`Private`\:041fW\:041f$$],
XMPTools`Wrappers`Private`\:041fW\:041f$$]],
Evaluate[XMPTools`Wrappers`Private`\:1586\:1587],
Evaluate[XMPTools`Wrappers`Private`\:1513\:1515], FrameTicks -> {
Range[(-16) Pi, 16 Pi, Pi/2],
Range[-1, 1, 1/2]}]}]),
"Specifications" :> {{{XMPTools`Wrappers`Private`\:15e9$$, 90}, 0,
360,
Rational[1, 256]}, {{XMPTools`Wrappers`Private`\:042fR$$,
Rational[1, 2], "\[CenterDot]|\[CenterDot]"}, 0, 1,
Rational[1, 256]}, {{
XMPTools`Wrappers`Private`\[CapitalPi]\[CapitalPi]$$, 8}, 0, 16,
1}, {{XMPTools`Wrappers`Private`\:041fW\:041f$$, 16}, 0, 64, 1}},
"Options" :> {FrameMargins -> 0}, "DefaultOptions" :> {}],
ImageSizeCache->{281., {312., 317.}},
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",
FontFamily->"Go Noto Current-Regular",
FontSize->10,ExpressionUUID->"87f7dffd-2a8e-4038-b9bf-2e250155a918"]
}, Open ]]
},
WindowSize->{1672, 980},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"12.2 for Microsoft Windows (64-bit) (December 12, 2020)",
StyleDefinitions->Notebook[{
Cell[
StyleData[StyleDefinitions -> "Default.nb"]],
Cell[
StyleData[All], TextAlignment -> Center, FontFamily ->
"Go Noto Current-Regular", FontSize -> 10, FontWeight -> "Normal",
FontSlant -> "Plain", FontTracking -> "Plain",
FontVariations -> {"StrikeThrough" -> False, "Underline" -> False}]},
Visible -> False, FrontEndVersion ->
"12.2 for Microsoft Windows (64-bit) (December 12, 2020)", StyleDefinitions ->
"PrivateStylesheetFormatting.nb"],
ExpressionUUID->"87e41aa9-dea0-4ea9-92c2-e68f9a3b2137"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 6723, 178, 499, "Input",ExpressionUUID->"670c0d5c-4772-49bb-b74f-ae6a69be9ed0"],
Cell[7284, 200, 6980, 185, 423, "Input",ExpressionUUID->"a4addeb7-2708-41df-8367-f56fd1c4c60d"],
Cell[CellGroupData[{
Cell[14289, 389, 7382, 181, 289, "Input",ExpressionUUID->"adf5a779-403a-4c2b-985b-3306f9c44e28"],
Cell[21674, 572, 6038, 117, 648, "Output",ExpressionUUID->"87f7dffd-2a8e-4038-b9bf-2e250155a918"]
}, Open ]]
}
]
*)