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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>
                  </items>
                  <chunks count="2">
                    <chunk name="Attributes">
                      <items count="5">
                        <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
                          <X>-520</X>
                          <Y>-605</Y>
                          <W>349</W>
                          <H>294</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>-519.5425</X>
                          <Y>-604.2982</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>
                    </chunk>
                  </chunks>
                </chunk>
              </chunks>
            </chunk>
            <chunk name="Object" index="13">
              <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">657af43c-250e-4e51-93c6-6810eb267706</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</item>
                    <item name="Source" index="0" type_name="gh_guid" type_code="9">74992216-b019-4116-a9c3-4c5aad3fb726</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>
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                          <W>161</W>
                          <H>294</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">
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                          <Y>651.6918</Y>
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                    </chunk>
                    <chunk name="PanelProperties">
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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">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>
                  </chunks>
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              </items>
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                    <item name="Description" type_name="gh_string" type_code="10">Format some data using placeholders and formatting tags</item>
                    <item name="InstanceGuid" type_name="gh_guid" type_code="9">14fc0b38-e972-49af-92fe-f7f422d34799</item>
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                    <item name="NickName" type_name="gh_string" type_code="10">Format</item>
                  </items>
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                          <X>370</X>
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                    </chunk>
                    <chunk name="ParameterData">
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                            <item name="Optional" type_name="gh_bool" type_code="1">false</item>
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                                  <chunks count="1">
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                                      </items>
                                    </chunk>
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                          <items count="6">
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                            <item name="InstanceGuid" type_name="gh_guid" type_code="9">4139ec23-7b86-4007-be98-c402dcf7c7ed</item>
                            <item name="Name" type_name="gh_string" type_code="10">Culture</item>
                            <item name="NickName" type_name="gh_string" type_code="10">Culture</item>
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              </items>
              <chunks count="1">
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                    <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>
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                        <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35">
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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>
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                          <ARGB>255;255;255;255</ARGB>
                        </item>
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                        <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>
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                        <item name="Wrap" type_name="gh_bool" type_code="1">true</item>
                      </items>
                    </chunk>
                  </chunks>
                </chunk>
              </chunks>
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              <items count="2">
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                <item name="Name" type_name="gh_string" type_code="10">Panel</item>
              </items>
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                  <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>
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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 name="DrawPaths" type_name="gh_bool" type_code="1">false</item>
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                        <item name="Wrap" type_name="gh_bool" type_code="1">true</item>
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