NestList Examples

NL=NestList[{Sin[2#1[[2]]]-Cos[3#1[[1]]],
Sin[2#1[[1]]]+Cos[#1[[2]]]}&,{-.5,.5},10^5];
ListPlot[NL,Axes->False,PlotStyle->Opacity[.1],
ColorFunction->Function[{x,y},Hue[x*y]],
ImageSize->500,AspectRatio->1,
Background->Lighter[Gray,.7]]

ReliefPlot Examples

With[{z=x+I y},ReliefPlot[Table[Cos[64#],
{x,##2},{y,##2}]&[If[Abs[z]>1.1 ,
0,#]&@Arg[Sum[(z(z^9+.01))^k!,
{k,4}]],-1.11,1.11,.005],
ImageSize->500,ColorFunction->"CoffeeTones"]]

Applying Accumulation

CL[k_,n_,alpha_]:=Accumulate[z=1;
Table[z=k*E^(#[[i]]I)z,
{i,n}]]&/@Tuples[{-alpha,alpha},n];
GCL=Function[{k,n,alpha},
Graphics[Table[{ColorData["CherryTones"][i/4],
Rotate[BSplineCurve@Transpose@{Re@#,
Im@#}&/@CL[k,n,alpha],i*Pi/2]},{i,4}],
ImageSize->400,Background->Lighter[Gray,.7]]];
{GCL[.7,10,Pi/4],GCL[.8,8,Pi/6]}

Examples of Dynamic Modules

DynamicModule[{cols,funs},
cols=RGBColor/@{"#3636ff","#ff3636"};
funs[y_,z_]:={{(1-z^4-Abs[y]^1.5)^2,y,z},
{-(1-z^4-Abs[y]^1.5)^2,y,z}};
Manipulate[Show[Table[ParametricPlot3D[funs[y,z],
{y,-(1 -z^4)^2,(1-z^4)^2},PlotRange->1,
Boxed->False,Axes->False,PlotPoints->100,
SphericalRegion->False,Background->RGBColor["#360036"],
PlotStyle->Blend[cols,(z+1)/2],ImageSize ->500,
ViewPoint->65 {1,0,1},ViewAngle ->Pi/256],
{z,-1+t,1-.001,.1}]],{t,.001,.1}]]

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]