Scratch

Graphics[Table[{x,y}={0,0};
p=1;
θ=RandomReal[{-π,π}];
Tooltip[{Hue[σ/1.3],Line[NestList[(θ+=RandomVariate[NormalDistribution[0,σ]];#+p {Cos[θ],Sin[θ]})&,{x,y},500]]},σ],{σ,0.1,1.2,0.1}]]

Accumulate[RandomChoice[{-1,1},10]]

Tuples[{-1,0,1},2]

Accumulate[RandomChoice[Tuples[{-1,0,1},2],10]]

ListLinePlot[Accumulate[RandomChoice[Tuples[{-1,0,1},2],50]],PlotStyle->Thick,ColorFunction->"NeonColors"]

ListLinePlot[Accumulate[RandomChoice[Tuples[{-1,0,1},2],50]],PlotStyle->Thick,ColorFunction->(CurveColor[#2]&)]

curve=KnotData["Trefoil","SpaceCurve"]
(*{Sin[#1]+2 Sin[2 #1],Cos[#1]-2 Cos[2 #1],-Sin[3 #1]}&*)

ParametricPlot3D[curve[t],{t,0,2 Pi},PlotStyle->AbsoluteThickness[10],ColorFunction->(CurveColor[#4]&),ColorFunctionScaling->True]

ColorFunction->(CurveColor[#4]&),

CurveColor[t_]:=Blend[{Color1,Color2,Color3,Color1},t]

CurveColor[t_]:=List@@Blend[{Color1,Color2,Color3},t]

CurveColor[phi_]:=List@@Blend[{Color1,Color2,Color3},Rescale[phi,{phimin,phimax}]]

Color1:=RGBColor[0.99,0.2,0.2,0.2];
Color2:=RGBColor[0.2,0.99,0.2,0.8];
Color3:=RGBColor[0.2,0.2,0.99,0.2];

Histogram[{1,2,1,0,1,0,1,2,1,2}]

RandomChoice[{-1,1}]

Module[{steps=1000},
Show[
ListLinePlot[{Range[0,steps],Join[{0},Accumulate[RandomChoice[{-1,0,1},steps]]]}\[Transpose],PlotStyle->{Thickness[Medium],Blue}]]]

Export["stock.eps",%332,"EPS"]

Manipulate[
Module[{colors,coeff},
colors={"AlizarinCrimson","Blue","DarkGreen","Orange","BlueViolet","TurquoiseBlue","Magenta","CinnabarGreen","Chocolate","DeepSkyBlue"};
coeff=Switch[prob,"50%",0.67449,"90%",1.64485,"95%",1.95996,"99%",2.57583,"99.9%",3.29053];
SeedRandom[seed];

Show[
Plot[{coeff Sqrt[n],-coeff Sqrt[n]},{n,0,steps},PlotRange->All,PlotStyle->Darker[Green,0.5]],
Table[ListLinePlot[{Range[0,steps],Join[{0},Accumulate[RandomChoice[{-1,1},steps]]]}\[Transpose],PlotStyle->{Thickness[Medium],ColorData["Legacy",colors[[i]]]}],{i,paths}],ImagePadding->{{25,15},{25,15}},ImageSize->{500,300}]],

{{steps,100,"steps"},100,10000,100,Appearance->"Labeled"},
{{paths,1,"paths"},1,10,1,Appearance->"Labeled"},
{{seed,1,"seed"},1,100,1,Appearance->"Labeled"},
{{prob,"95%","approximate confidence interval"},{"90%","95%","99%","99.9%"}}]

data=Import["T55test.WAV"][[1,1]];
signal=Transpose[Norm/@Partition[#,480]&/@data];

tpos=Range[Length[signal]];

tcolour=Blend[{{Min[tpos],Yellow},{Max[tpos],Red}},#]&;
tcolplot=Graphics[MapThread[{tcolour[#1],Point[#2]}&,{tpos,signal}],Axes->True,AspectRatio->1]

data=Accumulate[RandomChoice[Tuples[{-1,0,1},2],50]]

tpos=Range[50];
tcolour=Blend[{{Min[tpos],Yellow},{Max[tpos],Red}},#]&;

length=1000;
data=Join[{{0,0}},Accumulate[RandomChoice[Tuples[{-1,0,1},2],length]]];
tpos=Range[length];
tcolour=Blend[{{Min[tpos],Blue},{Max[tpos],Red}},#]&;Graphics[MapThread[{tcolour[#1],Point[#2],Line[{#2,#3}]}&,{tpos,Drop[data,-1],Drop[data,1]}],Axes->True,AspectRatio->1]

length=1000;
data=Join[{{0,0}},Accumulate[RandomChoice[Tuples[{-1,0,1},2],length]]];
tpos=Range[length];
tcolour=Blend[{{Min[tpos],Blue},{Max[tpos],Red}},#]&;Graphics[MapThread[{tcolour[#1],Line[{#2,#3}]}&,{tpos,Drop[data,-1],Drop[data,1]}],Axes->True,AspectRatio->1]

length=1000;
data=Join[{{0,0}},Accumulate[RandomChoice[Tuples[{-1,1},2],length]]];
tpos=Range[length];
tcolour=Blend[{{Min[tpos],Blue},{Max[tpos],Red}},#]&;Graphics[MapThread[{tcolour[#1],Line[{#2,#3}]}&,{tpos,Drop[data,-1],Drop[data,1]}],Axes->True,AspectRatio->1]

length=1000;
data=Join[{{0,0}},Accumulate[RandomChoice[{{0,-1},{0,1},{1,0},{-1,0}},length]]];
tpos=Range[length];
tcolour=Blend[{{Min[tpos],Blue},{Max[tpos],Red}},#]&;Graphics[{{EdgeForm[Black],White,Rectangle[{-50,-50},{50,50}]},MapThread[{tcolour[#1],Line[{#2,#3}]}&,{tpos,Drop[data,-1],Drop[data,1]}]},Axes->True,AspectRatio->1]

Manipulate[Module[{
grid={{0,-1},{0,1},{1,0},{-1,0}},
diag=Map[#/Norm[#]&,Drop[Tuples[{-1,0,1},2],{5}]],
MaxLength=1000},
SeedRandom[seed];data=Join[{{0,0}},Accumulate[RandomChoice[Switch[steps,1,grid,2,diag],MaxLength]]];
tpos=Range[MaxLength];
tcolour=Blend[{{Min[tpos],Blue},{Max[tpos],Red}},#]&;Graphics[{{EdgeForm[Black],White,Rectangle[{-50,-50},{50,50}]},MapThread[{tcolour[#1],Line[{#2,#3}]}&,{Take[tpos,length],Take[Drop[data,-1],length],Take[Drop[data,1],length]}]},Axes->True,AspectRatio->1]],{length,100,1000,100},{seed,1000,1050,1},{{steps,1},{1->"Grid",2->"Diagonals"}}]

Two-dimensional random walks

Manipulate[Module[{
grid={{0,-1},{0,1},{1,0},{-1,0}},
diag=Map[#/Norm[#]&,Drop[Tuples[{-1,0,1},2],{5}]],
MaxLength=1000},
SeedRandom[seed];data=Join[{{0,0}},Accumulate[Switch[steps,1,RandomChoice[grid,MaxLength],2,RandomChoice[diag,MaxLength],3,Map[{Cos[#],Sin[#]}&,RandomReal[{-π,π},1000]]]]];
tpos=Range[MaxLength];
tcolour=Blend[{{Min[tpos],Blue},{Max[tpos],Red}},#]&;Graphics[{{EdgeForm[Black],White,Rectangle[{-50,-50},{50,50}]},MapThread[{tcolour[#1],Line[{#2,#3}]}&,{Take[tpos,length],Take[Drop[data,-1],length],Take[Drop[data,1],length]}]},Axes->True,AspectRatio->1]],{length,100,1000,100},{seed,1000,1050,1},{{steps,1},{1->"Grid",2->"Diagonals",3->"Any Angle"}}]