Polar Plots & Parameters

PPIJK=Function[{i,j,k,t},
i*Log[(j+.9Cos[i^2*t])(1.01+Sin[k*t])]];
Show[Table[PolarPlot[PPIJK[i,j,7,t],{t,0,2Pi},
PlotStyle->Darker[Hue[(j-5)/5],.05i]],
{i,3,7},{j,6,10}],PlotRange->All,
ImageSize->500,Frame->True,Axes->False]

BrownianBridgeProcess VS RandomReal

RR=RandomReal[{-1.5,1.5},{101,3}]; SeedRandom[11];
RW=RandomFunction[BrownianBridgeProcess[{0,0},{1,1}],
{0, 1,.01},3]["ValueList"];
Graphics3D[Table[{Style[Tube[(Transpose@RW)[[i;;i+1]],.03],
ColorData["BrightBands"][.01i]],Style[Tube[RR[[i;;i+1]],.02],
ColorData["DarkBands"][.01i],Opacity[.2]]},{i,100}]]

Color Exploration

PDG[p_]:=Graphics3D[{Opacity[.3],
Tube[PolyhedronData[p,"Edges","Coordinates"],.05],
EdgeForm[Transparent],FaceForm[Opacity[.7],White],
Transpose[{ColorData["Crayola",
"ColorList"][[11;;10+Length[#]]],
#}]}]&@PolyhedronData[p,"Polygons"];
PDT[p_]:=Graphics3D[MapIndexed[Style[Text[ColorData["Crayola"][[3,
1,10+#2[[1]]]],#1],15]&,Mean/@(PolyhedronData[p,
"VertexCoordinates"][[#]]&/@PolyhedronData[p,"FaceIndices"])]];
Show[PDG[PolyhedronData["Archimedean"][[11]]],
PDT[PolyhedronData["Archimedean"][[11]]],
Boxed->False,ImageSize->700,ViewPoint->{-3,-1,3.5}]

Built-in Color Sets

Multicolumn[ColorData["Crayola",
"ColorRules"][[11;;80]],5]

Examples of Problem Solving

Pl[x1_,x2_]:=Plot[{-Log[x],-Log[x]*x},
{x,x1,x2},PlotStyle->{Blue,Magenta}];
Va[x_]:=Graphics[{Blue,Text[Style[N[-Log[x]*x],20],
{x+.1,-Log[x]+.1}],Opacity[.3],Polygon[{{0,0},
{x,0},{x,-Log[x]},{0,-Log[x]}}]}];
xmax=Solve[D[-Log[x]*x,x]\[Equal]0,x][[1,1,2]];
Vmax=Graphics[{Red,Text[Style[-Log[xmax]*xmax,30],
{xmax+.05,-Log[xmax]+.1}],Text[Style["*",30],
{xmax,-Log[xmax]*xmax-.1}],Opacity[.5],
Polygon[{{0,0},{xmax,0},
{xmax,-Log[xmax]},{0,-Log[xmax]}}]}];
Show[Pl[0,1.1],Vmax,Va[.15],Va[.65],
ImageSize->600,GridLines->Automatic]