Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 SectorTreePlot

Source Notebook

Plot tree data in stacked angular sectors

Contributed by: Giulio Alessandrini

ResourceFunction["SectorTreePlot"][tree]

plots the data in tree stacking child sectors radially.

Details and Options

SectorTreePlot can take all the options of Graphics with the following additions and modifications:
ColorFunctionAutomatichow to color the sectors
MethodAutomatichow to build the sectors
TreeElementLabelFunctionAutomatichow to label the sectors
The argument of the color function is an association with the following keys:
"Angle"the {min,max} angles of a sector (0,2π]
"Data"the tree data
"Label"the label speficied by the label function
"Level"the tree level
"Position"the tree position
"Step"the {min,max} angular step of a sector (0,1]
"Tree"the full input tree
The default color function is Hue[Mean[params["Step"]],1/params["Level"]+.3,.95] for positive levels and GrayLevel[.3] at level zero.
Possible values for Method are:
"Fixed"assign the same angular space to each child
"Value"assign space propotionally to the child data
The default TreeElementLabelFunction is Row[{edge,": ",data}] for labelled parent edges and simply data for unlabelled edges.

Examples

Basic Examples (1) 

Plot the tree data in nested sectors:

In[1]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[2, { Tree[1, { Tree[5, None]}], Tree[6, { Tree[4, None], Tree[9, None], Tree[7, None], Tree[3, None]}], Tree[8, { Tree[10, None]}]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.456928793535896, 1.2642542005660564`}, {0., 0.6321271002830282}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.456928793535896, 1.2642542005660564`}, { 1.456928793535896, 0.6321271002830282}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.456928793535896, 1.2642542005660564`}, { 2.913857587071792, 0.6321271002830282}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0., 0.6321271002830282}, {0., 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.456928793535896, 0.6321271002830282}, { 0.5827715174143585, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.456928793535896, 0.6321271002830282}, { 1.165543034828717, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.456928793535896, 0.6321271002830282}, { 1.7483145522430754`, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.456928793535896, 0.6321271002830282}, { 2.331086069657434, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.913857587071792, 0.6321271002830282}, { 2.913857587071792, 0.}}]}}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.456928793535896, 1.2642542005660564}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0., 0.6321271002830282}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["5", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.456928793535896, 0.6321271002830282}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["4", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.5827715174143585, 0.}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["9", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.165543034828717, 0.}], "DynamicName", BoxID -> "VertexID$6"], TagBox[InsetBox[ FrameBox["7", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.7483145522430754, 0.}], "DynamicName", BoxID -> "VertexID$7"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.331086069657434, 0.}], "DynamicName", BoxID -> "VertexID$8"], TagBox[InsetBox[ FrameBox["8", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.913857587071792, 0.6321271002830282}], "DynamicName", BoxID -> "VertexID$9"], TagBox[InsetBox[ FrameBox["10", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.913857587071792, 0.}], "DynamicName", BoxID -> "VertexID$10"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->{}, BaselinePosition->Automatic, ContentSelectable->Automatic, DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->{164.671875, Automatic}, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\)]
Out[1]=

Options (7) 

Background (1) 

Use a custom background:

In[2]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[4, { Tree[5, { Tree[3, None], Tree[2, None]}], Tree[6, None], Tree[1, None]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.2247448713915892`, 1.6546743414131073`}, { 0.4082482904638631, 0.8273371707065537}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.2247448713915892`, 1.6546743414131073`}, { 1.2247448713915892`, 0.8273371707065537}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.2247448713915892`, 1.6546743414131073`}, { 2.041241452319315, 0.8273371707065537}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.4082482904638631, 0.8273371707065537}, {0., 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.4082482904638631, 0.8273371707065537}, { 0.8164965809277261, 0.}}]}}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["4", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.2247448713915892, 1.6546743414131073}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["5", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.4082482904638631, 0.8273371707065537}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.8164965809277261, 0.}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.2247448713915892, 0.8273371707065537}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.041241452319315, 0.8273371707065537}], "DynamicName", BoxID -> "VertexID$6"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->{}, BaselinePosition->Automatic, ContentSelectable->Automatic, DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->None, FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), Background -> LightGray]
Out[2]=

ColorFunction (3) 

Use a hue that scales inversely with the level:

In[3]:=
SeedRandom[114]; ResourceFunction["SectorTreePlot"][RandomTree[100], ColorFunction -> (Hue[1/(#Level + 1)] &)]
Out[4]=

Use a hue proportional to the angle:

In[5]:=
ResourceFunction["SectorTreePlot"][Tree[0, Range[50]], ColorFunction -> (Hue[First[#Angle]/(2 Pi)] &)]
Out[5]=

Use a hue proportional to the scaled position:

In[6]:=
ResourceFunction["SectorTreePlot"][Tree[0, Range[50]], ColorFunction -> (Hue[First[#Step]] &)]
Out[6]=

These two are equivalent for equal size sectors:

In[7]:=
{ResourceFunction["SectorTreePlot"][Tree[0, ConstantArray[1, 50]], ColorFunction -> (Hue[First[#Angle]/(2 Pi)] &)], ResourceFunction["SectorTreePlot"][Tree[0, ConstantArray[1, 50]], ColorFunction -> (Hue[First[#Step]] &)]}
Out[7]=

Create a grayscale plot:

In[8]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[9, { Tree[5, { Tree[10, None], Tree[11, { Tree[8, None]}]}], Tree[2, None]}], Tree[12, { Tree[4, { Tree[3, { Tree[6, None]}], Tree[7, None]}]}]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 0.898520700674884, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 2.24630175168721, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 0.449260350337442, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 1.347781051012326, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, {0., 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, { 0.898520700674884, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 0.8830973267045875}, { 0.898520700674884, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 2.649291980113763}, { 2.24630175168721, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 1.797041401349768, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 2.695562102024652, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.797041401349768, 0.8830973267045875}, { 1.797041401349768, 0.}}]}}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.572411226181047, 3.5323893068183505}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["9", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["5", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.449260350337442, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["10", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["11", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["8", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.898520700674884, 0.}], "DynamicName", BoxID -> "VertexID$6"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.347781051012326, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$7"], TagBox[InsetBox[ FrameBox["12", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$8"], TagBox[InsetBox[ FrameBox["4", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$9"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.797041401349768, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$10"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.797041401349768, 0.}], "DynamicName", BoxID -> "VertexID$11"], TagBox[InsetBox[ FrameBox["7", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.695562102024652, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$12"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->{}, BaselinePosition->Automatic, ContentSelectable->Automatic, DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), ColorFunction -> (GrayLevel[First[#Step] + .1] &)]
Out[8]=

Method (3) 

By default, a numerical tree is plotted with sector angles proportional to the tree data:

In[9]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[9, { Tree[5, { Tree[10, None], Tree[11, { Tree[8, None]}]}], Tree[2, None]}], Tree[12, { Tree[4, { Tree[3, { Tree[6, None]}], Tree[7, None]}]}]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 0.898520700674884, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 2.24630175168721, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 0.449260350337442, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 1.347781051012326, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, {0., 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, { 0.898520700674884, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 0.8830973267045875}, { 0.898520700674884, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 2.649291980113763}, { 2.24630175168721, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 1.797041401349768, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 2.695562102024652, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.797041401349768, 0.8830973267045875}, { 1.797041401349768, 0.}}]}}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.572411226181047, 3.5323893068183505}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["9", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["5", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.449260350337442, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["10", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["11", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["8", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.898520700674884, 0.}], "DynamicName", BoxID -> "VertexID$6"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.347781051012326, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$7"], TagBox[InsetBox[ FrameBox["12", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$8"], TagBox[InsetBox[ FrameBox["4", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$9"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.797041401349768, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$10"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.797041401349768, 0.}], "DynamicName", BoxID -> "VertexID$11"], TagBox[InsetBox[ FrameBox["7", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.695562102024652, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$12"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->{}, BaselinePosition->Automatic, ContentSelectable->Automatic, DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\)]
Out[9]=

Use equal angles instead:

In[10]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[9, { Tree[5, { Tree[10, None], Tree[11, { Tree[8, None]}]}], Tree[2, None]}], Tree[12, { Tree[4, { Tree[3, { Tree[6, None]}], Tree[7, None]}]}]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 0.898520700674884, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 2.24630175168721, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 0.449260350337442, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 1.347781051012326, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, {0., 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, { 0.898520700674884, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 0.8830973267045875}, { 0.898520700674884, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 2.649291980113763}, { 2.24630175168721, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 1.797041401349768, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 2.695562102024652, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.797041401349768, 0.8830973267045875}, { 1.797041401349768, 0.}}]}}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.572411226181047, 3.5323893068183505}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["9", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["5", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.449260350337442, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["10", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["11", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["8", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.898520700674884, 0.}], "DynamicName", BoxID -> "VertexID$6"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.347781051012326, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$7"], TagBox[InsetBox[ FrameBox["12", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$8"], TagBox[InsetBox[ FrameBox["4", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$9"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.797041401349768, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$10"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.797041401349768, 0.}], "DynamicName", BoxID -> "VertexID$11"], TagBox[InsetBox[ FrameBox["7", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.695562102024652, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$12"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->{}, BaselinePosition->Automatic, ContentSelectable->Automatic, DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), Method -> "Fixed"]
Out[10]=

By default, a mixed numerical and non-numerical tree uses proportional angles when all the children of a tree have numerical data:

In[11]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[9, { Tree["e", { Tree[10, None], Tree["k", { Tree[8, None]}]}], Tree[2, None]}], Tree[12, { Tree["d", { Tree[3, { Tree[6, None]}], Tree[7, None]}]}]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 0.898520700674884, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 2.24630175168721, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 0.449260350337442, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 1.347781051012326, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, {0., 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, { 0.898520700674884, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 0.8830973267045875}, { 0.898520700674884, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 2.649291980113763}, { 2.24630175168721, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 1.797041401349768, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 2.695562102024652, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.797041401349768, 0.8830973267045875}, { 1.797041401349768, 0.}}]}}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.572411226181047, 3.5323893068183505}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["9", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["\<\"e\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.449260350337442, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["10", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["\<\"k\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["8", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.898520700674884, 0.}], "DynamicName", BoxID -> "VertexID$6"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.347781051012326, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$7"], TagBox[InsetBox[ FrameBox["12", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$8"], TagBox[InsetBox[ FrameBox["\<\"d\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$9"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.797041401349768, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$10"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.797041401349768, 0.}], "DynamicName", BoxID -> "VertexID$11"], TagBox[InsetBox[ FrameBox["7", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.695562102024652, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$12"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->{}, BaselinePosition->Automatic, ContentSelectable->Automatic, DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\)]
Out[11]=

Force equal angles:

In[12]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[9, { Tree["e", { Tree[10, None], Tree["k", { Tree[8, None]}]}], Tree[2, None]}], Tree[12, { Tree["d", { Tree[3, { Tree[6, None]}], Tree[7, None]}]}]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 0.898520700674884, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 2.24630175168721, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 0.449260350337442, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 1.347781051012326, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, {0., 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, { 0.898520700674884, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 0.8830973267045875}, { 0.898520700674884, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 2.649291980113763}, { 2.24630175168721, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 1.797041401349768, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 2.695562102024652, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.797041401349768, 0.8830973267045875}, { 1.797041401349768, 0.}}]}}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.572411226181047, 3.5323893068183505}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["9", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["\<\"e\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.449260350337442, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["10", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["\<\"k\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["8", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.898520700674884, 0.}], "DynamicName", BoxID -> "VertexID$6"], TagBox[InsetBox[ FrameBox["2", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.347781051012326, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$7"], TagBox[InsetBox[ FrameBox["12", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$8"], TagBox[InsetBox[ FrameBox["\<\"d\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$9"], TagBox[InsetBox[ FrameBox["3", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.797041401349768, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$10"], TagBox[InsetBox[ FrameBox["6", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.797041401349768, 0.}], "DynamicName", BoxID -> "VertexID$11"], TagBox[InsetBox[ FrameBox["7", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.695562102024652, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$12"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->{}, BaselinePosition->Automatic, ContentSelectable->Automatic, DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), Method -> "Fixed"]
Out[12]=

It is not possible to used proportional angles in this case:

In[13]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree[1, { Tree[9, { Tree["e", { Tree[10, None], Tree["k", { Tree[8, None]}]}], Tree[2, None]}], Tree[12, { Tree["d", { Tree[3, { Tree[6, None]}], Tree[7, None]}]}]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 0.898520700674884, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 2.24630175168721, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 0.449260350337442, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 1.347781051012326, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, {0., 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.449260350337442, 1.7661946534091753`}, { 0.898520700674884, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 0.8830973267045875}, { 0.898520700674884, 0.}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 2.649291980113763}, { 2.24630175168721, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 1.797041401349768, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{2.24630175168721, 1.7661946534091753`}, { 2.695562102024652, 0.8830973267045875}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.797041401349768, 0.8830973267045875}, { 1.797041401349768, 0.}}]}}, {Hue[0.6, 0.2, 0.8], EdgeForm[{GrayLevel[0], Opacity[0.7]}], TagBox[InsetBox[ FrameBox["1", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {1.572411226181047, 3.5323893068183505}], "DynamicName", BoxID -> "VertexID$1"], TagBox[InsetBox[ FrameBox["9", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 2.649291980113763}], "DynamicName", BoxID -> "VertexID$2"], TagBox[InsetBox[ FrameBox["\<\"e\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.449260350337442, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$3"], TagBox[InsetBox[ FrameBox["10", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["\<\"k\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["8", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], 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DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\), Method -> "Value"]
Out[13]=

By default, a mixed non-numerical tree uses equal angles:

In[14]:=
ResourceFunction["SectorTreePlot"][\!\(\* GraphicsBox[ NamespaceBox["Trees", DynamicModuleBox[{Typeset`tree = HoldComplete[ Tree["a", { Tree["i", { Tree["e", { Tree["j", None], Tree["k", { Tree["h", None]}]}], Tree["b", None]}], Tree["l", { Tree["d", { Tree["c", { Tree["f", None]}], Tree["g", None]}]}]}]]}, NamespaceBox[{ {Hue[0.6, 0.7, 0.5], Opacity[0.7], Arrowheads[Medium], {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 0.898520700674884, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{1.572411226181047, 3.5323893068183505`}, { 2.24630175168721, 2.649291980113763}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], LineBox[{{0.898520700674884, 2.649291980113763}, { 0.449260350337442, 1.7661946534091753`}}]}, {RGBColor[0.6, 0.5882352941176471, 0.5529411764705883], AbsoluteThickness[1], 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0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0., 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$4"], TagBox[InsetBox[ FrameBox["\<\"k\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {0.898520700674884, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$5"], TagBox[InsetBox[ FrameBox["\<\"h\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {0.898520700674884, 0.}], "DynamicName", BoxID -> "VertexID$6"], TagBox[InsetBox[ FrameBox["\<\"b\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.347781051012326, 1.7661946534091753}], "DynamicName", BoxID -> "VertexID$7"], TagBox[InsetBox[ FrameBox["\<\"l\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->4, StripOnInput->False], {2.24630175168721, 2.649291980113763}], 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FrameBox["\<\"f\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {1.797041401349768, 0.}], "DynamicName", BoxID -> "VertexID$11"], TagBox[InsetBox[ FrameBox["\<\"g\"\>", Background->Directive[ RGBColor[0.9607843137254902, 0.9882352941176471, 0.9764705882352941]], BaseStyle->GrayLevel[0], FrameMargins->{{2, 2}, {1, 1}}, FrameStyle->Directive[ RGBColor[0.4196078431372549, 0.6313725490196078, 0.4196078431372549], AbsoluteThickness[1], Opacity[1]], ImageSize->Automatic, RoundingRadius->0, StripOnInput->False], {2.695562102024652, 0.8830973267045875}], "DynamicName", BoxID -> "VertexID$12"]}}]]], AlignmentPoint->Center, Axes->False, AxesLabel->None, AxesOrigin->Automatic, AxesStyle->{}, Background->None, BaseStyle->{}, BaselinePosition->Automatic, ContentSelectable->Automatic, DefaultBaseStyle->"TreeGraphics", Epilog->{}, FormatType->StandardForm, Frame->False, FrameLabel->FormBox["False", StandardForm], FrameStyle->{}, FrameTicks->None, FrameTicksStyle->{}, GridLines->None, GridLinesStyle->{}, ImageMargins->0., ImagePadding->All, ImageSize->Automatic, LabelStyle->{}, PlotLabel->None, PlotRange->All, PlotRangeClipping->False, PlotRangePadding->Automatic, PlotRegion->Automatic, Prolog->{}, RotateLabel->True, Ticks->Automatic, TicksStyle->{}]\)]
Out[14]=

Applications (2) 

Build a tree from a nested symbolic expression:

In[15]:=
tree = ExpressionTree[a + b^Cos[e + 1] + c^3 + d + Cos[e]]
Out[15]=

Build a tree from a nested symbolic expression:

In[16]:=
ResourceFunction["SectorTreePlot"][tree]
Out[16]=

Build a tree of a region of the file system:

In[17]:=
tree = FileSystemTree[$InstallationDirectory, 3]
Out[17]=

Compute the size of all the files (the tree leaves):

In[18]:=
sizeTree = TreeMap[QuantityMagnitude[FileSize[#], "Megabytes"] &, tree, "Leaves"]
Out[18]=

Propagate the size up the tree:

In[19]:=
completeSizeTree = TreeMap[Total, sizeTree, "NonLeaves" -> "ChildrenData", TreeTraversalOrder -> "LeavesFirst"]
Out[19]=

Plot the tree in sectors:

In[20]:=
ResourceFunction["SectorTreePlot"][completeSizeTree]
Out[20]=

Version History

  • 1.0.0 – 01 May 2023

Related Resources

License Information