Surfaces as Exercises 4

MSPP2[a_,b_,c_,s_]:=Module[{x,y,z},
x=a(2+Cos[u])Cos[v]^3*Sin[v];
y=b(2+Cos[u+2Pi/3])Cos[v+2Pi/3]^2*Sin[v+2Pi/3]^2;
z=c(2+Cos[u-2Pi/3])Cos[v+2Pi/3]^2*Sin[v+2Pi/3]^2;
ParametricPlot3D[Table[{i*x,j*y,k*z},

{i,{-1,1}},{j,{-1,1}},{k,{-1,1}}],
{u,0,2Pi},{v,0,Pi},AspectRatio->1,

PlotRange->All,PlotPoints->20,
PlotStyle->Directive[RGBColor["steelblue"],

Opacity[.2]],Axes->False,Boxed->False,
Mesh->{20,20},MeshStyle->{White,Cyan},ImageSize->s,
Background->RGBColor["silver"]]];
MSPP2[1,1,1,600]

Surfaces as Exercises 3

MSPP[a_,b_,c_,d_,s_]:=Module[{h,x,y,z},
h=a(1+u^2Sin[v]^2); z=b(Cos[u]+u*Sin[u])Sin[v]/h;
y=b(-u*Cos[u]+Sin[u])Sin[v]/h; x=(Log[Tan[v/c]]/c+Cos[v]/h)/b;
ParametricPlot3D[{x,y,z},{u,-3Pi,3Pi},{v,d,Pi-d},PlotRange->All,
PlotStyle->{RGBColor["steelblue"],

Opacity[.1]},Axes->False,Boxed->False,
AspectRatio->1,ViewPoint->{.3,1,0},

PlotPoints->50,Mesh->{90,30},
MeshStyle->{White,Cyan},ImageSize->s,

Background->RGBColor["silver"]]];
MSPP[1,2,2,.001,600]

Surfaces as Exercises 2

CPP2[a_,b_,c_,s_]:=ParametricPlot3D[

{u*Cos[a*v],u*Sin[b*v],-v*Cos[c*u]},
{u,-2Pi,2Pi},{v,0,2Pi},PlotStyle->{RGBColor["steelblue"],

Opacity[.2]},Axes->False,Boxed->False,

AspectRatio->1,PlotRange->All,
ViewPoint->{.8,.8,.9},PlotPoints->50,
Mesh->{25,50},MeshStyle->{RGBColor["crimson"],Cyan},
ImageSize->s,Background->RGBColor["silver"]];
{CPP2[1,1,1,400],CPP2[4,-3,1,400]}

Surfaces as Exercises

CPP[a_,b_,c_,s_]:=ParametricPlot3D[

{a*Cos[v]Sinh[u]-b*Cos[c*v]Sinh[c*u],
a*Sin[v]Sinh[u]+b*Sin[c*v]Sinh[c*u],

Cos[a*v]Cosh[a*u]},
{u,-1,1},{v,-Pi,Pi},PlotStyle->{RGBColor["steelblue"],Opacity[.2]},
Axes->False,Boxed->False,AspectRatio->1,ViewPoint->{.1,0,2},
PlotRange->All,PlotPoints->50,
Mesh->{30,50},MeshStyle->{Magenta,Cyan},ImageSize->s,
Background->RGBColor["silver"]];
{CPP[2,.6,3,400],CPP[8,4,3,400]}

RecurrenceTable Examples 7

RALPC[a_,n_,s_,col_]:=Module[{rt},
rt=RecurrenceTable[{

x[i+1]==Re[a+(1-a)*(x[i]+I*y[i])],
y[i+1]==Im[a+(1-a)*(x[i]+I*y[i])],
x[0]==Re[(1+2I)*a],y[0]==Im[(1+2I)*a]},

{x,y},{i,1,n}];
ListPlot[rt,ColorFunction->col,Axes->False,

Background->RGBColor["black"],
ImageSize->s,AspectRatio->1]];
{RALPC[.01+.15I,100000,400,"BrightBands"],

RALPC[.05+.21I,100000,400,"NeonColors"]}