diff --git a/triangle_exponent_plots.m b/triangle_exponent_plots.m
index 33c4d4f69d668b1422514564df1dbd7b89a92ceb..64326401c0e5eb0e64b83e28df6ce7b64c4b5b58 100644
--- a/triangle_exponent_plots.m
+++ b/triangle_exponent_plots.m
@@ -26,7 +26,7 @@ gsraw=SortBy[gsraw,#[[1,1]]&]; (* Sort by n *)
 averagesGrouped=GatherBy[gsraw,{#[[1,2]]&,#[[1,1]]&}];
 
 
-gsraw2=Import[NotebookDirectory[]<>"data/graphdata_canonical_properties2.m"];
+gsraw2=Import[NotebookDirectory[]<>"data/graphdata_canonical_properties3.m"];
 gsraw2=SortBy[gsraw2,#[[1,1]]&]; (* Sort by n *)
 averagesGrouped2=GatherBy[gsraw2,{#[[1,2]]&,#[[1,1]]&}];
 canonicalDatapoints=Map[{#[[1,1,1]],Mean[#[[All,2]]]}&,averagesGrouped2,{2}];
@@ -34,7 +34,7 @@ canonicalDatapoints=Map[{#[[1,1,1]],Mean[#[[All,2]]]}&,averagesGrouped2,{2}];
 
 (* averagesGrouped[[ tau index, n index, run index , {ntau, avgtri} ]] *)
 nlabels=Map["n = "<>ToString[#]&,averagesGrouped[[1,All,1,1,1]]];
-taulabels=Map["tau = "<>ToString[#]&,averagesGrouped[[All,1,1,1,2]]];
+taulabels=Map["\[Tau] = "<>ToString[#]&,averagesGrouped[[All,1,1,1,2]]];
 mediansErrorBars=Map[
 {{#[[1,1,1]],Median[#[[All,2]]]},
 ErrorBar[MedianDeviation[#[[All,2]]]]
@@ -70,6 +70,7 @@ mediansFitsExtra=Map[LinearModelFit[#,logn,logn]&,mediansLoglogdata];
 
 canonicalloglogdata=Log[canonicalDatapoints[[All,nRange]]];
 canonicalFitsExtra=Map[LinearModelFit[#,logn,logn]&,canonicalloglogdata];
+canonicalFitFuncs=Map[#[logn]&,canonicalFitsExtra];
 canonicalNLMs=Map[NonlinearModelFit[#,factor*n^exponent,{factor,exponent},n]&,canonicalDatapoints];
 
 
@@ -79,11 +80,21 @@ averagesFitsExtra[[1]]["ParameterErrors"]
 averagesFitsExtra[[1]]["ParameterConfidenceIntervals"]
 
 
+tauChoices={1,3,5,7,9,11};
+canonicalTaulabels=Map["\[Tau] = "<>ToString[NumberForm[#,{4,2}]]&,averagesGrouped2[[tauChoices,1,1,1,2]]];
 plot1a=Show[ListLogLogPlot[averagesErrorBars[[All,All,1]],Joined->False,PlotMarkers->Automatic,AxesLabel->{"n","\[LeftAngleBracket]triangles\[RightAngleBracket]"},PlotLegends->taulabels],Plot[averagesFits,{logn,1,2000}]]
 plot1b=Show[ListLogLogPlot[mediansErrorBars[[All,All,1]],Joined->False,PlotMarkers->Automatic,AxesLabel->{"n","median triangles"},PlotLegends->taulabels],Plot[mediansFits,{logn,1,2000}]]
+plot1c=Show[ListLogLogPlot[canonicalDatapoints[[tauChoices]],
+ImageSize->250,
+Joined->False,PlotMarkers->Automatic,
+Frame->True,
+FrameTicks->{{Table[{10^k,Superscript[10,k]},{k,0,6}],Automatic},{{1000,2000,5000,10000},Automatic}},
+FrameLabel->{"n","triangles"},
+PlotLegends->canonicalTaulabels
+],Plot[Evaluate[canonicalFitFuncs[[tauChoices]]],{logn,1,20000}]]
 
 
-Export[NotebookDirectory[]<>"plots/avgtris_n.pdf",plot1]
+Export[NotebookDirectory[]<>"plots/avgtris_n.pdf",plot1c]
 
 
 (* ::Subsection:: *)
@@ -114,14 +125,17 @@ canonicalExponentsErrorBars=Map[{{#[[1]],#[[2]]["BestFitParameters"][[2]]},Error
 Transpose[{canonicalTauValues+0.000,canonicalFitsExtra}]];
 canonicalExponentsErrorBars2=Map[{{#[[1]],exponent/.#[[2]]["BestFitParameters"][[2]]},ErrorBar[#[[2]]["ParameterConfidenceIntervals"][[2]]-exponent/.#[[2]]["BestFitParameters"]]}&,
 Transpose[{canonicalTauValues+0.000,canonicalNLMs}]];
+
+Needs["MaTeX`"]
+
 plot2=Show[
-ErrorListPlot[{averagesExponentsErrorBars,mediansExponentsErrorBars,canonicalExponentsErrorBars},
+ErrorListPlot[{averagesExponentsErrorBars(*,mediansExponentsErrorBars*),canonicalExponentsErrorBars},
 Joined->True,PlotMarkers->Automatic,
-PlotLegends->Placed[{"average","median","canonical"},{Left,Bottom}],
+PlotLegends->Placed[{"average"(*,"median"*),"canonical"},{Left,Bottom}],
 Frame->True,FrameLabel->{"tau","triangle exponent"},
 PlotRange->{{2,3},{0,1.6}},
 ImageSize->300],
-Plot[3/2(3-tau),{tau,2,3},PlotStyle->{Black,Dashed}]]
+Plot[3/2(3-tau),{tau,2,3},PlotStyle->{Black,Dashed},PlotLegends->Placed[LineLegend[{MaTeX["\\frac{3}{2}(3-\\tau)"]},LegendMarkerSize->20],{Left,Bottom}]]]
 
 
 Export[NotebookDirectory[]<>"plots/triangle_exponent.pdf",plot2]