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If blank, all occurences of F will be removed.</item> + <item name="InstanceGuid" type_name="gh_guid" type_code="9">0b09f73d-3b76-4872-b23e-af65f6ccf7e0</item> + <item name="Name" type_name="gh_string" type_code="10">Replace</item> + <item name="NickName" type_name="gh_string" type_code="10">Replace</item> + <item name="Optional" type_name="gh_bool" type_code="1">true</item> + <item name="SourceCount" type_name="gh_int32" type_code="3">0</item> + </items> + <chunks count="1"> + <chunk name="Attributes"> + <items count="2"> + <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35"> + <X>642</X> + <Y>329</Y> + <W>39</W> + <H>20</H> + </item> + <item name="Pivot" type_name="gh_drawing_pointf" type_code="31"> + <X>661.5</X> + <Y>339</Y> + </item> + </items> + </chunk> + </chunks> + </chunk> + <chunk name="param_output" index="0"> + <items count="6"> + <item name="Description" type_name="gh_string" type_code="10">Result of text replacement</item> + <item name="InstanceGuid" 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</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">56223043-f43a-42ef-985f-d78d63756e0d</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">1</item> + <item name="Source" index="0" type_name="gh_guid" type_code="9">b0ba83ad-8597-47a1-8b7d-06bc1ac8e14c</item> + <item name="SourceCount" type_name="gh_int32" type_code="3">1</item> + <item name="UserText" type_name="gh_string" type_code="10">Double click to edit panel contentβ¦</item> + </items> + <chunks count="2"> + <chunk name="Attributes"> + <items count="5"> + <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35"> + <X>893</X> + <Y>227</Y> + <W>422</W> + <H>230</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>893.2493</X> + <Y>227.1955</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="12"> + <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="8"> + <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">757d8d62-c94b-4f14-9c46-fabb75b95b88</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">1</item> + <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 &), {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[#]} & /. 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)] & /@ f; + ParametricPlot[ + Evaluate[#[tplot] & /@ 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<0,Return[0,Module]];tol=10^(-prec); +z=SetPrecision[x,Infinity];s=1;y=0; +z=If[0<=z<=2,1-Abs[1-z],q=Quotient[z,2]; +If[ThueMorse[q]==1,s=-1]; +1-Abs[1-z+2 q]]; +While[z>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]<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] &, Denominator][x] == 0], False] := iFabiusF[x]; +Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &; +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<0,Return[0,Module]];tol=10^(-prec); +z=SetPrecision[x,Infinity];s=1;y=0; +z=If[0<=z<=2,1-Abs[1-z],q=Quotient[z,2]; +If[ThueMorse[q]==1,s=-1]; +1-Abs[1-z+2 q]]; +While[z>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]<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] &, Denominator][x] == 0], False] := iFabiusF[x]; +Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &; +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> + <chunks count="2"> + <chunk name="Attributes"> + <items count="5"> + <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35"> + <X>176</X> + <Y>651</Y> + <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"> + <X>176.1313</X> + <Y>651.6918</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> + </chunks> + </chunk> + </chunks> + </chunk> + <chunk name="Object" index="14"> + <items count="2"> + <item name="GUID" type_name="gh_guid" type_code="9">758d91a0-4aec-47f8-9671-16739a8a2c5d</item> + <item name="Name" type_name="gh_string" type_code="10">Format</item> + </items> + <chunks count="1"> + <chunk name="Container"> + <items count="4"> + <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> + <item name="Name" type_name="gh_string" type_code="10">Format</item> + <item name="NickName" type_name="gh_string" type_code="10">Format</item> + </items> + <chunks count="2"> + <chunk name="Attributes"> + <items count="2"> + <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35"> + <X>370</X> + <Y>630</Y> + <W>88</W> + <H>64</H> + </item> + <item name="Pivot" type_name="gh_drawing_pointf" type_code="31"> + <X>420</X> + <Y>662</Y> + </item> + </items> + </chunk> + <chunk name="ParameterData"> + <items count="6"> + <item name="InputCount" type_name="gh_int32" type_code="3">3</item> + <item name="InputId" index="0" type_name="gh_guid" type_code="9">3ede854e-c753-40eb-84cb-b48008f14fd4</item> + <item name="InputId" index="1" type_name="gh_guid" type_code="9">7fa15783-70da-485c-98c0-a099e6988c3e</item> + <item name="InputId" index="2" type_name="gh_guid" type_code="9">8ec86459-bf01-4409-baee-174d0d2b13d0</item> + <item name="OutputCount" type_name="gh_int32" type_code="3">1</item> + <item name="OutputId" index="0" type_name="gh_guid" type_code="9">3ede854e-c753-40eb-84cb-b48008f14fd4</item> + </items> + <chunks count="4"> + <chunk name="InputParam" index="0"> + <items count="6"> + <item name="Description" type_name="gh_string" type_code="10">Text format</item> + <item name="InstanceGuid" type_name="gh_guid" type_code="9">2f5b811b-689d-4e1b-9ea3-ffc7fcfe7ef9</item> + <item name="Name" type_name="gh_string" type_code="10">Format</item> + <item name="NickName" type_name="gh_string" type_code="10">Format</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> + <chunks count="2"> + <chunk name="Attributes"> + <items count="2"> + <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35"> + <X>372</X> + <Y>632</Y> + <W>36</W> + <H>20</H> + </item> + <item name="Pivot" type_name="gh_drawing_pointf" type_code="31"> + <X>390</X> + <Y>642</Y> + </item> + </items> + </chunk> + <chunk name="PersistentData"> + <items count="1"> + <item name="Count" type_name="gh_int32" type_code="3">1</item> + </items> + <chunks count="1"> + <chunk name="Branch" index="0"> + <items count="2"> + <item name="Count" type_name="gh_int32" type_code="3">1</item> + <item name="Path" type_name="gh_string" type_code="10">{0}</item> + </items> + <chunks count="1"> + <chunk name="Item" index="0"> + <items count="2"> + <item name="null_string" type_name="gh_bool" type_code="1">false</item> + <item name="string" type_name="gh_string" type_code="10">{0:R}</item> + </items> + </chunk> + </chunks> + </chunk> + </chunks> + </chunk> + </chunks> + </chunk> + <chunk name="InputParam" index="1"> + <items count="6"> + <item name="Description" type_name="gh_string" type_code="10">Formatting culture</item> + <item name="InstanceGuid" type_name="gh_guid" type_code="9">4139ec23-7b86-4007-be98-c402dcf7c7ed</item> + <item name="Name" type_name="gh_string" 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type_name="gh_guid" type_code="9">c12585f7-fe64-4c0f-869d-d10df254cf72</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">b731122a-226d-4448-829a-f10aac320680</item> + <item name="SourceCount" type_name="gh_int32" type_code="3">1</item> + </items> + <chunks count="1"> + <chunk name="Attributes"> + <items count="2"> + <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35"> + <X>631</X> + <Y>524</Y> + <W>50</W> + <H>24</H> + </item> + <item name="Pivot" type_name="gh_drawing_pointf" type_code="31"> + <X>656</X> + <Y>536</Y> + </item> + </items> + </chunk> + </chunks> + </chunk> + </chunks> + </chunk> + <chunk name="Object" index="17"> + <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="8"> + <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> + <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">1</item> + <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 &), {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[#]} & /. 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)] & /@ f; + ParametricPlot[ + Evaluate[#[tplot] & /@ 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<0,Return[0,Module]];tol=10^(-prec); +z=SetPrecision[x,Infinity];s=1;y=0; +z=If[0<=z<=2,1-Abs[1-z],q=Quotient[z,2]; +If[ThueMorse[q]==1,s=-1]; +1-Abs[1-z+2 q]]; +While[z>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]<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] &, Denominator][x] == 0], False] := iFabiusF[x]; +Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &; +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]]; + +Π = CurvaturePlot[ + Evaluate[ + SetPrecision[SetAccuracy[Abs[FabiusF[X/Pi*((((4))))/2]], Infinity], + Infinity], {X, 0, 4 \[Pi]}, WorkingPrecision -> ((((10)))), + Accuracy -> Infinity, MaxRecursion -> 0, PlotPoints -> 1 + 2^((((8))))], + Axes -> {True, True}]; +Show[Π, Frame -> True, FrameTicks -> {{-1, 0, 1}, {-1, 0, 1}}, + PlotRange -> Full, AspectRatio -> 1]; +βΠβ = Flatten[Cases[Π, Line[X__] -> X, Infinity], 1]; +Export["βΠβ", βΠβ, "CSV"]; +βΠβ</item> + </items> + <chunks count="2"> + <chunk name="Attributes"> + <items count="5"> + <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35"> + <X>-629</X> + <Y>330</Y> + <W>349</W> + <H>671</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>-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> + </chunk> + </chunks> + </chunk> + </chunks> + </chunk> + <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<0,Return[0,Module]];tol=10^(-prec); +z=SetPrecision[x,Infinity];s=1;y=0; +z=If[0<=z<=2,1-Abs[1-z],q=Quotient[z,2]; +If[ThueMorse[q]==1,s=-1]; +1-Abs[1-z+2 q]]; +While[z>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]<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] &, Denominator][x] == 0], False] := iFabiusF[x]; +Derivative[n_Integer][FabiusF] := 2^(n (n + 1)/2) FabiusF[2^n #] &; +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> + <chunks count="2"> + <chunk name="Attributes"> + <items count="5"> + <item name="Bounds" type_name="gh_drawing_rectanglef" type_code="35"> + <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" 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</bitmap> 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