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OOOO/𖣠⚪ᗩ∣ↀ∣𒾨⚪𔗢⚪🞋⚪𔗢⚪𒾨∣ↀ∣ᗩ⚪𖣠/𖣠⚪✤ᴥᗩ⚪𔗢⚪🞋⚪𔗢⚪ᗩᴥ✤⚪𖣠/𖣠⚪ᗱᗴᴥᗩᗯ✤ꗳⓄᔓᔕ⚪𔗢⚪🞋⚪𔗢⚪ᔓᔕⓄꗳ✤ᗯᗩᴥ.../𖣠⚪ᕭᕮᗩНߦᗱᗴᙏᕭᕮⓄߦ✤⚪𔗢⚪🞋⚪𔗢⚪✤ߦⓄᕭᕮ.../𖣠⚪ᔓᔕⓄᴥᗱᗴᑐᑕⓄИNꖴ옷ᴥ⚪𔗢⚪🞋⚪𔗢⚪ᴥ옷ꖴИ.../𖣠⚪ᴥᗱᗴߦⓄ옷ᔓᔕᗩᴥᕤᕦ⚪𔗢⚪🞋⚪𔗢⚪ᕤᕦᴥᗩᔓᔕ.../XHꓨ..⚪ᗩ⚪ᑐᑕ⚪ꖴ⚪✤⚪ᗩ⚪ᙏ⚪ᗱᗴ⚪옷⚪✤⚪ᗩ...

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XHꓨ..⚪ᗩ⚪ᑐᑕ⚪ꖴ⚪✤⚪ᗩ⚪ᙏ⚪ᗱᗴ⚪옷⚪✤⚪ᗩ⚪ᙏ⚪◌⚪◌⚪◌⚪◌⚪◌⚪◌⚪ᙏ⚪ᗩ⚪✤⚪옷⚪ᗱᗴ⚪ᙏ⚪ᗩ⚪✤⚪ꖴ⚪ᑐᑕ⚪ᗩ⚪..GHX
9 months ago
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<item name="UserText" type_name="gh_string" type_code="10">ClearAll[iCurvaturePlotHelper, CurvaturePlot]
iCurvaturePlotHelper[
f_?(Head[#] =!= List &amp;), {t_, tmin_,
tmax_}, {{x0_, y0_}, \[Theta]0_}, opts : OptionsPattern[]] :=
Module[{sol, \[Theta], x, y, if},
sol = NDSolve[{
\[Theta]'[t] == f,
x'[t] == Cos[\[Theta][t]],
y'[t] == Sin[\[Theta][t]],
\[Theta][tmin] == \[Theta]0,
x[tmin] == x0,
y[tmin] == y0
}, {x, y}, {t, tmin, tmax}, opts];
if = {x[#], y[#]} &amp; /. First[sol];
if
]
CurvaturePlot[f_, {t_, tmin_, tmax_}, opts : OptionsPattern[]] :=
CurvaturePlot[f, {t, tmin, tmax}, {{0, 0}, 0}, opts]
CurvaturePlot[f_, {t_, tmin_, tmax_}, p : {{x0_, y0_}, \[Theta]0_},
opts : OptionsPattern[]] :=
Module[{\[Theta], x, y, sol, rlsplot, rlsndsolve, if, ifs},
rlsplot = FilterRules[{opts}, Options[ParametricPlot]];
rlsndsolve = FilterRules[{opts}, Options[NDSolve]];
If[Head[f] === List,
ifs =
iCurvaturePlotHelper[#, {t, tmin, tmax}, p,
Evaluate@(Sequence @@ rlsndsolve)] &amp; /@ f;
ParametricPlot[
Evaluate[#[tplot] &amp; /@ ifs], {tplot, tmin, tmax},
Evaluate@(Sequence @@ rlsplot)]
,
if =
iCurvaturePlotHelper[f, {t, tmin, tmax}, p,
Evaluate@(Sequence @@ rlsndsolve)];
ParametricPlot[Evaluate[if[tplot]], {tplot, tmin, tmax},
Evaluate@(Sequence @@ rlsplot)]
]
];
ariasD[0] = 1;
ariasD[n_Integer?Positive] := ariasD[n] = Sum[2^((k (k - 1) - n (n - 1))/2) ariasD[k]/(n - k + 1)!, {k, 0, n - 1}]/(2^n - 1);
iFabiusF[x_]:=Module[{prec=Precision[x],n,p,q,s,tol,w,y,z},If[x&lt;0,Return[0,Module]];tol=10^(-prec);
z=SetPrecision[x,Infinity];s=1;y=0;
z=If[0&lt;=z&lt;=2,1-Abs[1-z],q=Quotient[z,2];
If[ThueMorse[q]==1,s=-1];
1-Abs[1-z+2 q]];
While[z&gt;0,n=-Floor[RealExponent[z,2]];p=2^n;
z-=1/p;w=1;
Do[w=ariasD[m]+p z w/(n-m+1);p/=2,{m,n}];
y=w-y;
If[Abs[w]&lt;Abs[y] tol,Break[]]];
SetPrecision[s Abs[y],prec]];
FabiusF[Infinity] = Interval[{-1, 1}];
FabiusF[x_?NumberQ] /; If[Im[x] == 0, TrueQ[Composition[BitAnd[#, # - 1] &amp;, Denominator][x] == 0], False] := iFabiusF[x];
Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &amp;;
SetAttributes[FabiusF, {NumericFunction, Listable}];//Timing//AbsoluteTiming;
ToString[DecimalForm[N[Table[{ToString[DecimalForm[N[X],256]],ToString[DecimalForm[N[FabiusF[X]],256]],ToString[DecimalForm[N[0],256]]},{X,0,N[1],N[1/16]}]],256]]</item>
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<item name="MarginRight" type_name="gh_int32" type_code="3">0</item>
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<item name="Colour" type_name="gh_drawing_color" type_code="36">
<ARGB>255;255;255;255</ARGB>
</item>
<item name="DrawIndices" type_name="gh_bool" type_code="1">true</item>
<item name="DrawPaths" type_name="gh_bool" type_code="1">true</item>
<item name="Multiline" type_name="gh_bool" type_code="1">true</item>
<item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
<item name="Stream" type_name="gh_bool" type_code="1">false</item>
<item name="Wrap" type_name="gh_bool" type_code="1">true</item>
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<item name="UserText" type_name="gh_string" type_code="10">ariasD[0] = 1;
ariasD[n_Integer?Positive] := ariasD[n] = Sum[2^((k (k - 1) - n (n - 1))/2) ariasD[k]/(n - k + 1)!, {k, 0, n - 1}]/(2^n - 1);
iFabiusF[x_]:=Module[{prec=Precision[x],n,p,q,s,tol,w,y,z},If[x&lt;0,Return[0,Module]];tol=10^(-prec);
z=SetPrecision[x,Infinity];s=1;y=0;
z=If[0&lt;=z&lt;=2,1-Abs[1-z],q=Quotient[z,2];
If[ThueMorse[q]==1,s=-1];
1-Abs[1-z+2 q]];
While[z&gt;0,n=-Floor[RealExponent[z,2]];p=2^n;
z-=1/p;w=1;
Do[w=ariasD[m]+p z w/(n-m+1);p/=2,{m,n}];
y=w-y;
If[Abs[w]&lt;Abs[y] tol,Break[]]];
SetPrecision[s Abs[y],prec]];
FabiusF[Infinity] = Interval[{-1, 1}];
FabiusF[x_?NumberQ] /; If[Im[x] == 0, TrueQ[Composition[BitAnd[#, # - 1] &amp;, Denominator][x] == 0], False] := iFabiusF[x];
Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &amp;;
SetAttributes[FabiusF, {NumericFunction, Listable}];//Timing//AbsoluteTiming;
ToString[DecimalForm[N[Table[{ToString[DecimalForm[N[t],256]],ToString[DecimalForm[N[FabiusF[t]],256]],ToString[DecimalForm[N[0],256]]},{t,0,N[1],N[1/32]}]],256]]</item>
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</item>
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<item name="Multiline" type_name="gh_bool" type_code="1">true</item>
<item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
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<item name="Name" type_name="gh_string" type_code="10">Culture</item>
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<item name="InstanceGuid" type_name="gh_guid" type_code="9">c12585f7-fe64-4c0f-869d-d10df254cf72</item>
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</items>
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<chunk name="Container">
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<item name="Description" type_name="gh_string" type_code="10">A panel for custom notes and text values</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">32ca42c3-b85d-40fc-b02f-a79187312f7b</item>
<item name="Name" type_name="gh_string" type_code="10">Panel</item>
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<item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
<item name="UserText" type_name="gh_string" type_code="10">ClearAll[iCurvaturePlotHelper, CurvaturePlot]
iCurvaturePlotHelper[
f_?(Head[#] =!= List &amp;), {t_, tmin_,
tmax_}, {{x0_, y0_}, \[Theta]0_}, opts : OptionsPattern[]] :=
Module[{sol, \[Theta], x, y, if},
sol = NDSolve[{
\[Theta]'[t] == f,
x'[t] == Cos[\[Theta][t]],
y'[t] == Sin[\[Theta][t]],
\[Theta][tmin] == \[Theta]0,
x[tmin] == x0,
y[tmin] == y0
}, {x, y}, {t, tmin, tmax}, opts];
if = {x[#], y[#]} &amp; /. First[sol];
if
]
CurvaturePlot[f_, {t_, tmin_, tmax_}, opts : OptionsPattern[]] :=
CurvaturePlot[f, {t, tmin, tmax}, {{0, 0}, 0}, opts]
CurvaturePlot[f_, {t_, tmin_, tmax_}, p : {{x0_, y0_}, \[Theta]0_},
opts : OptionsPattern[]] :=
Module[{\[Theta], x, y, sol, rlsplot, rlsndsolve, if, ifs},
rlsplot = FilterRules[{opts}, Options[ParametricPlot]];
rlsndsolve = FilterRules[{opts}, Options[NDSolve]];
If[Head[f] === List,
ifs =
iCurvaturePlotHelper[#, {t, tmin, tmax}, p,
Evaluate@(Sequence @@ rlsndsolve)] &amp; /@ f;
ParametricPlot[
Evaluate[#[tplot] &amp; /@ ifs], {tplot, tmin, tmax},
Evaluate@(Sequence @@ rlsplot)]
,
if =
iCurvaturePlotHelper[f, {t, tmin, tmax}, p,
Evaluate@(Sequence @@ rlsndsolve)];
ParametricPlot[Evaluate[if[tplot]], {tplot, tmin, tmax},
Evaluate@(Sequence @@ rlsplot)]
]
];
ariasD[0] = 1;
ariasD[n_Integer?Positive] := ariasD[n] = Sum[2^((k (k - 1) - n (n - 1))/2) ariasD[k]/(n - k + 1)!, {k, 0, n - 1}]/(2^n - 1);
iFabiusF[x_]:=Module[{prec=Precision[x],n,p,q,s,tol,w,y,z},If[x&lt;0,Return[0,Module]];tol=10^(-prec);
z=SetPrecision[x,Infinity];s=1;y=0;
z=If[0&lt;=z&lt;=2,1-Abs[1-z],q=Quotient[z,2];
If[ThueMorse[q]==1,s=-1];
1-Abs[1-z+2 q]];
While[z&gt;0,n=-Floor[RealExponent[z,2]];p=2^n;
z-=1/p;w=1;
Do[w=ariasD[m]+p z w/(n-m+1);p/=2,{m,n}];
y=w-y;
If[Abs[w]&lt;Abs[y] tol,Break[]]];
SetPrecision[s Abs[y],prec]];
FabiusF[Infinity] = Interval[{-1, 1}];
FabiusF[x_?NumberQ] /; If[Im[x] == 0, TrueQ[Composition[BitAnd[#, # - 1] &amp;, Denominator][x] == 0], False] := iFabiusF[x];
Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &amp;;
SetAttributes[FabiusF, {NumericFunction, Listable}];//Timing//AbsoluteTiming;
ToString[DecimalForm[N[Table[{ToString[DecimalForm[N[X],256]],ToString[DecimalForm[N[FabiusF[X]],256]],ToString[DecimalForm[N[0],256]]},{X,0,N[1],N[1/256]}]],256]];
П = CurvaturePlot[
Evaluate[
SetPrecision[SetAccuracy[Abs[FabiusF[X/Pi*((((4))))/2]], Infinity],
Infinity], {X, 0, 4 \[Pi]}, WorkingPrecision -&gt; ((((10)))),
Accuracy -&gt; Infinity, MaxRecursion -&gt; 0, PlotPoints -&gt; 1 + 2^((((8))))],
Axes -&gt; {True, True}];
Show[П, Frame -&gt; True, FrameTicks -&gt; {{-1, 0, 1}, {-1, 0, 1}},
PlotRange -&gt; Full, AspectRatio -&gt; 1];
ↀПↀ = Flatten[Cases[П, Line[X__] -&gt; X, Infinity], 1];
Export["ↀПↀ", ↀПↀ, "CSV"];
ↀПↀ</item>
</items>
<chunks count="2">
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<item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
<X>-629</X>
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</item>
<item name="MarginLeft" type_name="gh_int32" type_code="3">0</item>
<item name="MarginRight" type_name="gh_int32" type_code="3">0</item>
<item name="MarginTop" type_name="gh_int32" type_code="3">0</item>
<item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
<X>-628.7882</X>
<Y>330.9467</Y>
</item>
</items>
</chunk>
<chunk name="PanelProperties">
<items count="7">
<item name="Colour" type_name="gh_drawing_color" type_code="36">
<ARGB>255;255;255;255</ARGB>
</item>
<item name="DrawIndices" type_name="gh_bool" type_code="1">true</item>
<item name="DrawPaths" type_name="gh_bool" type_code="1">true</item>
<item name="Multiline" type_name="gh_bool" type_code="1">true</item>
<item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
<item name="Stream" type_name="gh_bool" type_code="1">false</item>
<item name="Wrap" type_name="gh_bool" type_code="1">true</item>
</items>
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<chunk name="Object" index="18">
<items count="2">
<item name="GUID" type_name="gh_guid" type_code="9">59e0b89a-e487-49f8-bab8-b5bab16be14c</item>
<item name="Name" type_name="gh_string" type_code="10">Panel</item>
</items>
<chunks count="1">
<chunk name="Container">
<items count="9">
<item name="Description" type_name="gh_string" type_code="10">A panel for custom notes and text values</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">d540c611-1af7-4e7e-9179-d4927d03008d</item>
<item name="Name" type_name="gh_string" type_code="10">Panel</item>
<item name="NickName" type_name="gh_string" type_code="10"></item>
<item name="Optional" type_name="gh_bool" type_code="1">false</item>
<item name="ScrollRatio" type_name="gh_double" type_code="6">0.50049507617950439</item>
<item name="Source" index="0" type_name="gh_guid" type_code="9">b731122a-226d-4448-829a-f10aac320680</item>
<item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
<item name="UserText" type_name="gh_string" type_code="10">ariasD[0] = 1;
ariasD[n_Integer?Positive] := ariasD[n] = Sum[2^((k (k - 1) - n (n - 1))/2) ariasD[k]/(n - k + 1)!, {k, 0, n - 1}]/(2^n - 1);
iFabiusF[x_]:=Module[{prec=Precision[x],n,p,q,s,tol,w,y,z},If[x&lt;0,Return[0,Module]];tol=10^(-prec);
z=SetPrecision[x,Infinity];s=1;y=0;
z=If[0&lt;=z&lt;=2,1-Abs[1-z],q=Quotient[z,2];
If[ThueMorse[q]==1,s=-1];
1-Abs[1-z+2 q]];
While[z&gt;0,n=-Floor[RealExponent[z,2]];p=2^n;
z-=1/p;w=1;
Do[w=ariasD[m]+p z w/(n-m+1);p/=2,{m,n}];
y=w-y;
If[Abs[w]&lt;Abs[y] tol,Break[]]];
SetPrecision[s Abs[y],prec]];
FabiusF[Infinity] = Interval[{-1, 1}];
FabiusF[x_?NumberQ] /; If[Im[x] == 0, TrueQ[Composition[BitAnd[#, # - 1] &amp;, Denominator][x] == 0], False] := iFabiusF[x];
Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &amp;;
SetAttributes[FabiusF, {NumericFunction, Listable}];//Timing//AbsoluteTiming;
ToString[DecimalForm[N[Table[{ToString[DecimalForm[N[t],256]],ToString[DecimalForm[N[FabiusF[t]],256]],ToString[DecimalForm[N[0],256]]},{t,0,N[1],N[1/32]}]],256]]</item>
</items>
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<X>-260</X>
<Y>521</Y>
<W>200</W>
<H>289</H>
</item>
<item name="MarginLeft" type_name="gh_int32" type_code="3">0</item>
<item name="MarginRight" type_name="gh_int32" type_code="3">0</item>
<item name="MarginTop" type_name="gh_int32" type_code="3">0</item>
<item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
<X>-259.466</X>
<Y>521.5567</Y>
</item>
</items>
</chunk>
<chunk name="PanelProperties">
<items count="7">
<item name="Colour" type_name="gh_drawing_color" type_code="36">
<ARGB>255;255;255;255</ARGB>
</item>
<item name="DrawIndices" type_name="gh_bool" type_code="1">true</item>
<item name="DrawPaths" type_name="gh_bool" type_code="1">false</item>
<item name="Multiline" type_name="gh_bool" type_code="1">true</item>
<item name="SpecialCodes" type_name="gh_bool" type_code="1">false</item>
<item name="Stream" type_name="gh_bool" type_code="1">false</item>
<item name="Wrap" type_name="gh_bool" type_code="1">true</item>
</items>
</chunk>
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<item name="Name" type_name="gh_string" type_code="10">Replace Text</item>
</items>
<chunks count="1">
<chunk name="Container">
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<item name="Description" type_name="gh_string" type_code="10">Replace all occurences of a specific text fragment with another</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">cc216dbe-7368-4ad0-b361-9576424dcc24</item>
<item name="Name" type_name="gh_string" type_code="10">Replace Text</item>
<item name="NickName" type_name="gh_string" type_code="10">Replace Text</item>
<item name="RecursiveReplace" type_name="gh_bool" type_code="1">false</item>
</items>
<chunks count="5">
<chunk name="Attributes">
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<item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
<X>288</X>
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</item>
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<X>341</X>
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</item>
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</chunk>
<chunk name="param_input" index="0">
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<item name="Description" type_name="gh_string" type_code="10">Text to operate on.</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">5cd71bb6-669e-4d72-a523-2cdb216701d2</item>
<item name="Name" type_name="gh_string" type_code="10">Text</item>
<item name="NickName" type_name="gh_string" type_code="10">Text</item>
<item name="Optional" type_name="gh_bool" type_code="1">false</item>
<item name="Source" index="0" type_name="gh_guid" type_code="9">3f3d8116-c897-4cc1-8f26-d9cfbf2afd3a</item>
<item name="SourceCount" type_name="gh_int32" type_code="3">1</item>
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<chunk name="param_input" index="1">
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<item name="Description" type_name="gh_string" type_code="10">Fragment to replace.</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">e1c09eab-68b7-48e7-957e-87030b47bda3</item>
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<item name="Optional" type_name="gh_bool" type_code="1">true</item>
<item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
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<chunks count="2">
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<item name="Pivot" type_name="gh_drawing_pointf" type_code="31">
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</chunk>
<chunk name="PersistentData">
<items count="1">
<item name="Count" type_name="gh_int32" type_code="3">1</item>
</items>
<chunks count="1">
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<chunks count="1">
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<chunk name="param_input" index="2">
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<item name="Description" type_name="gh_string" type_code="10">Optional fragment to replace with. If blank, all occurences of F will be removed.</item>
<item name="InstanceGuid" type_name="gh_guid" type_code="9">2e47c43c-8894-49f7-a14f-1b3fea26d3e0</item>
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</item>
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</chunk>
</chunks>
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</chunks>
</chunk>
</chunks>
</chunk>
<chunk name="param_output" index="0">
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<item name="InstanceGuid" type_name="gh_guid" type_code="9">61005a47-bf72-44ac-b2ee-58fe4593ead5</item>
<item name="Name" type_name="gh_string" type_code="10">Result</item>
<item name="NickName" type_name="gh_string" type_code="10">Result</item>
<item name="Optional" type_name="gh_bool" type_code="1">false</item>
<item name="SourceCount" type_name="gh_int32" type_code="3">0</item>
</items>
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</item>
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<X>368.5</X>
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</item>
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</chunks>
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<item name="NickName" type_name="gh_string" type_code="10">Replace Text</item>
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<chunk name="param_input" index="1">
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<item name="Description" type_name="gh_string" type_code="10">Fragment to replace.</item>
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<chunk name="Thumbnail">
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