O
/
OOOO
mirror of http://CODE.RHODECODE.COM/u/O/O/O
1
0
Fork 0
Code Releases Activity
                                       ◦⸰◦○◦⸰◦◯◦⸰◦○◦⸰◦                     ⚪                     ◦⸰◦○◦⸰◦◯◦⸰◦○◦⸰◦                                       
You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
5131 Commits
1 Branch
2 Tags
5.0 GiB
Branch: ⠀
Branches Tags
${ item.name }
Create tag ${ searchTerm }
Create branch ${ searchTerm }
from '⠀'
${ noResults }
OOOO/∣❁∣ᙁᑐᑕ∣옷∣ᑐᑕᙁ∣❁∣/ᕤᕦИNⵙ✤ᑎߦᙏⓄᑐᑕⓄᙏߦᑎ✤ⵙИNᕤᕦ/ᗱᗴᴥᗩᗯ✤ꗳⓄᔓᔕⓄꗳ✤ᗯᗩᴥᗱᗴ/ᙏᗩᴥꗳᙁⓄᗯⓄᙁꗳᴥᗩᙏ/ᗩᑐᑕⵙ✤ᗩᙏᗱᗴ옷✤ᗩᙏᗩ✤옷ᗱᗴᙏᗩ✤ⵙᑐᑕᗩ/ᗺИ.𖣠⚪𔗢⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᗩ⚪ᙁ⚪ᑎ⚪ߦ⚪ꖴ⚪И...

763 lines
30 KiB
Raw Permalink Normal View History Unescape

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
9 months ago
(* 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[ 29251, 754]
NotebookOptionsPosition[ 27548, 714]
NotebookOutlinePosition[ 28951, 750]
CellTagsIndexPosition[ 28908, 747]
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->"Segoe UI Symbol",
FontSize->10,
FontWeight->"Normal",
CellLabel->
"3/24/24 14:22:34 \
In[760]:=",ExpressionUUID->"296ee68d-611b-4f39-8505-8dc995c0ca11"],
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",
TextAlignment->Center,
FontFamily->"Segoe UI Symbol",
FontSize->10,
FontWeight->"Normal",
CellLabel->"3/24/24 14:53:08 In[986]:=",
CellID->161896613,ExpressionUUID->"0d96d3fd-dac5-4a15-921c-c113c196ee35"],
Cell[CellGroupData[{
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"}], "]"}]}]}], " ", "}"}]}],
";"}], "\[IndentingNewLine]",
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"}], "]"}], "]"}]}], ";"}], "\[IndentingNewLine]",
RowBox[{"Grid", "[",
RowBox[{"{",
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{"Manipulate", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Column", "[",
RowBox[{"{", "\[IndentingNewLine]",
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]"}]}]}]}], "]"}],
"\[IndentingNewLine]", ",", "\[IndentingNewLine]",
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]"}]}]}]}], " ",
"]"}]}], "\[IndentingNewLine]", "}"}], "]"}], "\[IndentingNewLine]",
",", "\[IndentingNewLine]",
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"}], "}"}], "\[IndentingNewLine]", ",",
RowBox[{"FrameMargins", "\[Rule]", "0"}]}], "\[IndentingNewLine]",
"]"}], "\[IndentingNewLine]", "}"}], "}"}], "]"}]}], "Input",
TextAlignment->Center,
FontFamily->"Segoe UI Symbol",
FontSize->10,
FontWeight->"Normal",ExpressionUUID->"e9af63b5-ce7c-4f02-8437-ec7c3b69790f"],
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., 227.}}, 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]$$, 8}, 0, 16,
1}}, "Options" :> {FrameMargins -> 0}, "DefaultOptions" :> {}],
ImageSizeCache->{345., {340., 345.}},
SingleEvaluation->True],
Deinitialization:>None,
DynamicModuleValues:>{},
SynchronousInitialization->True,
UndoTrackedVariables:>{Typeset`show$$, 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->"Segoe UI Symbol",
FontSize->10,
CellLabel->
"3/24/24 17:03:33 \
Out[1958]=",ExpressionUUID->"d798a34d-f2da-42c6-8aa3-1c805195e5c5"]
}, Open ]]
},
WindowToolbars->"EditBar",
WindowSize->{1680, 984},
WindowMargins->{{-4, Automatic}, {Automatic, -4}},
FrontEndVersion->"12.2 for Microsoft Windows (64-bit) (December 12, 2020)",
StyleDefinitions->Notebook[{
Cell[
StyleData[StyleDefinitions -> "Default.nb"], TextAlignment -> Center,
FontFamily -> "Segoe UI Symbol", FontSize -> 12, FontWeight -> "Normal",
FontSlant -> "Plain", FontTracking -> "Plain",
FontVariations -> {"StrikeThrough" -> False, "Underline" -> False}],
Cell[
CellGroupData[{
Cell[
StyleData[All], TextAlignment -> Center, FontFamily ->
"Segoe UI Symbol", FontSize -> 12, FontWeight -> "Normal", FontSlant ->
"Plain", FontTracking -> "Plain",
FontVariations -> {"StrikeThrough" -> False, "Underline" -> False}],
Cell[
BoxData[""], "Input", TextAlignment -> Center, FontFamily ->
"Segoe UI Symbol", FontSize -> 12, FontWeight -> "Normal"]}, Open]]},
WindowSize -> {786, 884},
WindowMargins -> {{140, Automatic}, {-107, Automatic}}, FrontEndVersion ->
"12.2 for Microsoft Windows (64-bit) (December 12, 2020)", StyleDefinitions ->
"PrivateStylesheetFormatting.nb"],
ExpressionUUID->"5ef6097c-72c8-4d11-b3dd-efe77ae843c3"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 6715, 178, 400, "Input",ExpressionUUID->"296ee68d-611b-4f39-8505-8dc995c0ca11"],
Cell[7276, 200, 6600, 181, 325, "Input",ExpressionUUID->"0d96d3fd-dac5-4a15-921c-c113c196ee35",
CellID->161896613],
Cell[CellGroupData[{
Cell[13901, 385, 9380, 235, 236, "Input",ExpressionUUID->"e9af63b5-ce7c-4f02-8437-ec7c3b69790f"],
Cell[23284, 622, 4248, 89, 718, "Output",ExpressionUUID->"d798a34d-f2da-42c6-8aa3-1c805195e5c5"]
}, Open ]]
}
]
*)