In[]:=
NestGraph[x|->If[x<2,{1},{x-1,x-2}],6,10,VertexLabelsAutomatic]
Out[]=
In[]:=
NestGraph[x|->If[x<2,{1},{x^2-1,x-2}],2,5,VertexLabelsAutomatic]
Out[]=

3n+1 problem

In[]:=
NestGraph[x|->If[EvenQ[x],{x/2},{3x+1}],100,10,VertexLabelsAutomatic]
Out[]=
In[]:=
NestGraph[x|->If[Mod[x,3]==1,(x-1)/3,2x],100,10,VertexLabelsAutomatic]
Out[]=
In[]:=
NestGraph[x|->{If[Mod[x,3]==1,(x-1)/3,Nothing],2x},1,10,VertexLabelsAutomatic]
Out[]=
In[]:=
NestGraph[x|->{If[Mod[x,3]==1,(x-1)/3,Nothing],2x},1,20]
Out[]=
In[]:=
Solve[3x+1==y,x]
Out[]=
x
1
3
(-1+y)
In[]:=
Table
1
3
(-1+y),{y,10}
Out[]=
0,
1
3
,
2
3
,1,
4
3
,
5
3
,2,
7
3
,
8
3
,3
In[]:=
Options[TokenEventGraph]
Out[]=
{AllSubsetsTrue,TokenDeduplicationTrue,TokenMultiplicity1,AlignmentPointCenter,AnnotationRules{},AspectRatioAutomatic,AxesFalse,AxesLabelNone,AxesOriginAutomatic,AxesStyle{},BackgroundNone,BaselinePositionAutomatic,BaseStyle{},ContentSelectableAutomatic,DirectedEdgesAutomatic,EdgeCapacityAutomatic,EdgeCostAutomatic,EdgeLabelsNone,EdgeLabelStyleAutomatic,EdgeShapeFunctionAutomatic,EdgeStyleAutomatic,EdgeWeightAutomatic,EditableFalse,Epilog{},FormatTypeTraditionalForm,FrameFalse,FrameLabelNone,FrameStyle{},FrameTicksNone,FrameTicksStyle{},GraphHighlight{},GraphHighlightStyleAutomatic,GraphLayoutAutomatic,GraphRootAutomatic,GraphStyleAutomatic,GridLinesNone,GridLinesStyle{},ImageMargins0.,ImagePaddingAll,ImageSizeAutomatic,LabelStyle{},PerformanceGoalAutomatic,PlotLabelNone,PlotRangeAll,PlotRangeClippingFalse,PlotRangePaddingAutomatic,PlotRegionAutomatic,PlotThemeAutomatic,Prolog{},Properties{},RotateLabelTrue,TicksAutomatic,TicksStyle{},VertexCapacityAutomatic,VertexCoordinatesAutomatic,VertexLabelsNone,VertexLabelStyleAutomatic,VertexShapeAutomatic,VertexShapeFunctionAutomatic,VertexSizeAutomatic,VertexStyleAutomatic,VertexWeightAutomatic,EventDeduplicationFalse,TokenLabelingTrue,EventLabelingNone,TokenRenderingFunctionIdentity}
In[]:=
TokenEventGraph[{{n_}:>{n+1,n+2}},{1},4,"EventDeduplication"->True]
Out[]=
In[]:=
TokenEventGraph[{{n_}:>{n+1,n+2}},{1},4,"EventDeduplication"->False]
Out[]=