diff --git a/triangle_canonical_mixingtime.m b/triangle_canonical_mixingtime.m
index cb8ff6ad2e8391563f88f11de4691def6141c1e9..08f52fab664f79e78f60d1b5a0117648398ddca5 100644
--- a/triangle_canonical_mixingtime.m
+++ b/triangle_canonical_mixingtime.m
@@ -1,57 +1,152 @@
 (* ::Package:: *)
 
-gsraw=Import[NotebookDirectory[]<>"data/graphdata_canonical_mixingtime.m"];
+gsraw=Import[NotebookDirectory[]<>"data/graphdata_canonical_mixingtime_histogram.m"];
 gdata=GatherBy[gsraw,{#[[1,2]]&}];
 (* Data format: *)
 (* gdata[[ tau index, n index, datatype index ]] *)
 (* datatype index:
 1: {n,tau}
-2: { {time1, {samples1}}, {time2, {samples2}} , ... }
+2: { {time1, {samples1}}, {time2, {samples2}} , ... }  samples can also be a HistogramList kind of list
 3: {uniform samples}
 *)
 
 
-choices={1,2,3,6,8,12,14};
 (*Histogram[histogramdata[[All,2]],Automatic,"Probability",ChartLegends\[Rule]histogramdata[[All,1]]]*)
 
-makeHistogram[run_,choices_]:=Module[{gridsize,labels},
-gridsize=Max[0.5,Mean[run[[3]]]/200];
-labels="t = "<>ToString[#/run[[1,1]]]<>"\[CenterDot]n"&/@run[[2,choices,1]];
+makeHistogram[run_,plotrange_,choices_]:=Module[{gridsize,labels,wd,uni},
+uni=WeightedData[run[[3,All,1]],run[[3,All,2]]];(* Only in case of histogram-type file input *)
+gridsize=Max[1,Mean[uni]/100];
+labels="t = "<>ToString[NumberForm[N[#/run[[1,1]]],{3,1}]]<>" n"&/@run[[2,choices,1]];
+wd=run[[2,choices,2]];
+wd=Map[WeightedData[#[[All,1]],#[[All,2]]]&,wd];(* Only in case of histogram-type file input *)
 Show[
-SmoothHistogram[run[[2,choices,2]],gridsize,PlotRange->{All,Automatic},PlotLegends->labels,PlotLabel->"n = "<>ToString[run[[1,1]]],ImageSize->500],
-SmoothHistogram[run[[3]],gridsize,PlotLegends->{"uniform"},PlotStyle->{Thick,Black}]]]
+SmoothHistogram[wd,gridsize,
+PlotRange->plotrange,
+PlotLegends->Placed[labels,Scaled[{0.7,0.7}]],
+Epilog->Text["n = "<>ToString[run[[1,1]]]<>", \[Tau] = "<>ToString[run[[1,2]]],Scaled[{0.15,0.95}]],
+ImageSize->300,
+Frame->True,
+FrameLabel->{"triangles","probability"}
+],
+SmoothHistogram[uni,gridsize,PlotRange->plotrange,PlotLegends->Placed[{"uniform"},Scaled[{0.7,0.7}]],PlotStyle->{Thick,Black}]]]
 
-makeHistogram[gdata[[1,-1]],choices]
-makeHistogram[gdata[[-1,-1]],choices]
+normalize[h_]:=Transpose[{h[[All,1]],h[[All,2]]/Total[h[[All,2]]]}];
+
+makeHistogram2[run_,plotrange_,choices_]:=Module[{gridsize,labels,uni,probs},
+uni=WeightedData[run[[3,All,1]],run[[3,All,2]]];(* Only in case of histogram-type file input *)
+labels="t = "<>ToString[NumberForm[N[#/run[[1,1]]],{3,1}]]<>" n"&/@run[[2,choices,1]];
+probs=run[[2,choices,2]];
+probs=Map[normalize,probs];
+Show[
+ListPlot[probs,Joined->True,
+PlotRange->plotrange,
+PlotLegends->Placed[labels,Scaled[{0.7,0.7}]],
+Epilog->Text["n = "<>ToString[run[[1,1]]]<>", \[Tau] = "<>ToString[run[[1,2]]],Scaled[{0.15,0.95}]],
+ImageSize->300,
+Frame->True,
+FrameLabel->{"triangles","probability"}
+],
+ListPlot[normalize[run[[3]]],Joined->True,PlotRange->plotrange,PlotLegends->Placed[{"uniform"},Scaled[{0.7,0.7}]],PlotStyle->{Thick,Black}]]]
+
+plot1=makeHistogram[gdata[[1,-1]],{{3500,7800},{0,0.005}},{10,50,100}]
+plot2=makeHistogram2[gdata[[3,-1]],{{50,300},{0,0.04}},{10,20,30}]
+plot3=makeHistogram2[gdata[[5,-1]],{{0,70},{0,0.18}},{5,10,20}]
+
+
+Export[NotebookDirectory[]<>"plots/triangle_distributions_over_time.pdf",plot2]
+
+
+(* ::Section:: *)
+(*Total variation distance*)
 
 
 (* Get some sort of total variation distance between to sets of samples *)
-getTVDistance[samples1_,samples2_]:=Module[{max,probs1,probs2},
+getTVDistance1[samples1_,samples2_]:=Module[{max,probs1,probs2,binsize},
 max=Max[Max[samples1],Max[samples2]];
-probs1=BinCounts[samples1,{0,max+1,1}];
+binsize=Max[1,Floor[Mean[samples2]/500]];
+binsize=1;
+probs1=BinCounts[samples1,{0,max+binsize,binsize}];
 probs1=probs1/Total[probs1];
-probs2=BinCounts[samples2,{0,max+1,1}];
+probs2=BinCounts[samples2,{0,max+binsize,binsize}];
 probs2=probs2/Total[probs2];
 Total[Abs[probs1-probs2]]/2
 ]
 
 
-getRatios[run_]:=Module[{avg,sd,scalefactor},
+(* Get some sort of total variation distance between to HistogramList-like objects *)
+getTVDistance2[hist1_,hist2_]:=Module[{m,M,probs,probs1,probs2},
+m=Min[hist1[[1,1]],hist2[[1,1]]];
+M=Max[hist1[[-1,1]],hist2[[-1,1]]];
+probs=ConstantArray[0,M-m+1];
+probs1=hist1[[All,2]];
+probs1=probs1/Total[probs1];
+probs2=hist2[[All,2]];
+probs2=probs2/Total[probs2];
+probs[[1+hist1[[1,1]]-m;;1+hist1[[-1,1]]-m]]+=probs1;
+probs[[1+hist2[[1,1]]-m;;1+hist2[[-1,1]]-m]]-=probs2;
+Total[Abs[probs]]/2
+]
+
+
+(* ::Subsection:: *)
+(*Plots*)
+
+
+(*getRatios[run_]:=Module[{avg,sd,scalefactor},
 avg=Mean[run[[3]]];
 sd=StandardDeviation[run[[3]]];
-scalefactor=1/(run[[1,1]]*Log[run[[1,1]]]^0);
+scalefactor=1/(run[[1,1]]*Log[2,run[[1,1]]]^(1*(4-run[[1,2]])));
 {"n,tau = "<>ToString[run[[1]]],
 Map[{#[[1]]*scalefactor,Mean[#[[2]]]/avg}&,run[[2]]],
 Map[{#[[1]]*scalefactor,(Mean[#[[2]]]-avg)/sd}&,run[[2]]],
-Map[{#[[1]]*scalefactor,getTVDistance[#[[2]],run[[3]]]}&,run[[2]]]
 }
 ]
 ratios=Map[getRatios,gdata,{2}];
+(*Map[ListPlot[#[[All,2]],Joined->True,PlotMarkers->Automatic,PlotRange->(1+{-0.15,+0.15}),PlotLegends->#[[All,1]],ImageSize->300]&,ratios]*)
+(*Map[ListPlot[#[[All,3]],Joined->True,PlotMarkers->Automatic,PlotRange->(0+{-1,+1}),PlotLegends->#[[All,1]],ImageSize->300]&,ratios]*)
+*)
+getTVDs[run_]:=Module[{scalefactor},
+scalefactor=1/(run[[1,1]]*Log[2,run[[1,1]]]^(1*(4-run[[1,2]])));
+{"\[Tau] = "<>ToString[run[[1,2]]],
+Map[{#[[1]]*scalefactor,getTVDistance2[#[[2]],run[[3]]]}&,run[[2]]]}
+]
+TVDs=Map[getTVDs,gdata,{2}];
+
+
+Map[Show[ListPlot[#[[All,2]],
+Joined->True,(*PlotMarkers->Automatic,*)
+PlotLegends->#[[All,1]],ImageSize->500,
+PlotRange->{0,1},Frame->True,FrameLabel->{"steps / (n (\!\(\*SubscriptBox[\(log\), \(2\)]\)n\!\(\*SuperscriptBox[\()\), \(4 - \[Tau]\)]\))","TV distance"}],
+Plot[{0.1,0.05},{x,0,20},PlotStyle->Directive[Black,Dashed]]
+]&,TVDs]
 
 
-Map[ListPlot[#[[All,2]],Joined->True,PlotMarkers->Automatic,PlotRange->(1+{-0.15,+0.15}),PlotLegends->#[[All,1]],ImageSize->300]&,ratios]
-Map[ListPlot[#[[All,3]],Joined->True,PlotMarkers->Automatic,PlotRange->(0+{-1,+1}),PlotLegends->#[[All,1]],ImageSize->300]&,ratios]
-Map[ListPlot[#[[All,4]],Joined->True,PlotMarkers->Automatic,PlotRange->({0,1}),PlotLegends->#[[All,1]],ImageSize->300]&,ratios]
+(* ::Subsection:: *)
+(*Mixing time from TV distance*)
 
 
+getMixingTime[run_]:=Module[{i=1,timestamp=0,prevtimestamp=0},
+While[i<=Length[run[[2]]],
+    timestamp=run[[2,i,1]];
+    If[getTVDistance2[run[[2,i,2]],run[[3]]]<=0.1,
+        Break[];
+    ];
+    prevtimestamp=timestamp;
+    i++;
+];
+{run[[1,1]],run[[1,2]],prevtimestamp, timestamp} (* Range in which mixingtime lies *)
+]
+mixingtimes=Map[getMixingTime,gdata,{2}];
+
 
+scaling[n_,tau_]:=n*Log[n]^(4-tau);
+scaling[n_,tau_]:=n;
+plotData=Map[{#[[1]],#[[4]]/scaling[#[[1]],#[[2]]]}&,mixingtimes,{2}]~Join~Map[{#[[1]],#[[3]]/scaling[#[[1]],#[[2]]]}&,mixingtimes,{2}];
+fillings={1->{6},2->{7},3->{8},4->{9},5->{10}};
+taulabels=Map["\[Tau] = "<>ToString[#[[1,2]]]&,mixingtimes];
+ListPlot[plotData,
+Joined->True,PlotMarkers->Automatic,ImageSize->500,
+PlotRange->All,
+PlotLegends->taulabels,
+Filling->fillings,PlotStyle->{Automatic,Automatic,Automatic,Automatic,Automatic,None,None,None,None,None},
+Frame->True,FrameLabel->{"n","ETMT / n"}]