t+1/2 Log[((Cosh[j+x])/(Cosh[j-x]))]

Manipulate[Plot[{x,t+1/2 Log[((Cosh[j+x])/(Cosh[j-x]))]},{x,-2,2},PlotRange->{-2,2},AspectRatio->1],{{t,0},-2,2},{{j,0},-2,2}]

pl=ArrayPlot[Table[FixedPoint`itersConv[a,b,.51,.01],{a,0,1,.002},{b,0,1,.002}],DataReversed->True]

pl=ArrayPlot[Table[FixedPoint`itersConv[a,b,.51,.01],{a,0,1.5,.002},{b,0,1.5,.002}],DataReversed->True]

Table[Plot[{x,-4(x-a)(x-b)},{x,0,1}],{a,0,1,.34},{b,0,1,.34}]//GraphicsGrid

FixedPoint`itersConv[0,1,.51,.01]

Clear[fixedPoint]

(* takes function, starting point, iterations, returns list of points *)
fpList[f_,x0_,n_]:=Module[{pointlist,pointpairs,pointp,pointpp},
pointlist=NestList[f,x0, n];
pointpairs=Partition[Partition[pointlist, 2, 1],2,1];
(* insert projections to y=x *)
pointp=Flatten[{#1, {#2[[1]], #1[[2]]}, #2}& @@@pointpairs,{1,2,3}];
pointpp=Partition[pointp,2]
]

fixedPoint[f_, x0_,n_] := Module[{plot,lines1,lines2},
plot=Graphics[{Gray, Thickness[0.01], Line[{{-2,-2},{2,2}}],
Line[Table[{x,f[x]},{x,-2,2,0.01}]]}];
lines1=Graphics[{Red}~Join~{Line[fpList[f,x0,n]]}];
Show[{plot,lines1},PlotRange->{{-2,2},{-2,2}}]
]

fixedPoint[-4(#-0)(#-0)&,.2,5]

fixedPoint[-4(#-a)(#-b)&,.2,5]/.{a->.1,b->.9}

Table[fixedPoint[-4(#-a)(#-b)&,.51,7],{a,0.1,1.5,.25},{b,0.1,1.5,.25}]//GraphicsGrid

Manipulate[Plot[{x,-4(x-a)(x-b)},{x,0,1}],{{a,0},0,1},{{b,1},0,1}]

Table[fixedPoint[4(#-a)(#-b)&,.51,7],{a,0.1,1,.25},{b,0.1,1,.25}]//GraphicsGrid

(* takes function, starting point, iterations, returns list of points *)
fpList[f_,x0_,n_]:=Module[{pointlist,pointpairs,pointp,pointpp},
pointlist=NestList[f,x0, n];
pointpairs=Partition[Partition[pointlist, 2, 1],2,1];
(* insert projections to y=x *)
pointp=Flatten[{#1, {#2[[1]], #1[[2]]}, #2}& @@@pointpairs,{1,2,3}];
pointpp=Partition[pointp,2]
];
fixedPoint[f_, x0_,n_] := Module[{plot,lines1,lines2},
plot=Graphics[{Gray, Thickness[0.01], Line[{{-2,-2},{2,2}}],
Line[Table[{x,f[x]},{x,-2,2,0.01}]]}];
lines1=Graphics[{Red,Opacity[.8]}~Join~{Line[Clip[fpList[f,x0,n],{-10,10}]]}];
Show[{plot,lines1},PlotRange->{{-2,2},{-2,2}}]
]

pl=ArrayPlot[Table[FixedPoint`itersConv[a,b,.51,.01],{a,-1,0,.002},{b,0,1,.002}],DataReversed->True]

GraphicsGrid[Table[fixedPoint[-4(#-a)(#-b)&,.51,10],{a,-1,0,.1},{b,0.1,1,.1}],ImageSize->{600,600}]

Table[fixedPoint[t+1/2 Log[((Cosh[j+#])/(Cosh[j-#]))]&,0.51,10],{t,-1,1,.2},{j,-1,1,.2}]//Reverse[#]&//GraphicsGrid[#,ImageSize->{600,600}]&

Needs["JLink`"];
ReinstallJava[CommandLine->"C:\\Program Files\\Java\\jdk1.6.0_02\\bin\\java.exe"];
AddToClassPath[ToFileName[NotebookDirectory[]]];
LoadJavaClass["FixedPoint"];

Table[FixedPoint`itersConv2[t,j,0.51,.0001],{t,-1,1,.005},{j,-1,1,.005}]//ArrayPlot[#,DataReversed->True]&

SetDirectory[NotebookDirectory[]]

Export["blogpost.html",SelectedNotebook[]]