A bimbó

bimbi[x_]:= Exp[-6x^(1/2)]x^(1/2)

ParametricPlot3D[{Cos[u]bimbi[v]+Exp[-v],Sin[u]bimbi[v],-2Sin[v/2]},{u,0,2π},{v,0,π}, PlotRange->1,Axes->None,Mesh->None]

A közepe

kozep[x_]:=Cos[2x]

ParametricPlot3D[{Cos[u]kozep[v],Sin[u]kozep[v],Sin[v]Cos[v]},{u,0,2π}, {v,0,π},PlotRange->2]

Virág

ParametricPlot3D[{
{Cos[u]/(v^3-v^2-1/2*v-1),Sin[u]/(v^3-v^2-1/2*v-1),v},
{Cos[u]bimbi[-v]+Exp[v]/2,Sin[u]bimbi[-v],Sin[v]+0.3},
{Cos[u]bimbi[-v]-Exp[v]/2,Sin[u]bimbi[-v],Sin[v]+0.3},
{Cos[u]bimbi[-v],Sin[u]bimbi[-v]+Exp[v]/2,Sin[v]+0.3},
{Cos[u]bimbi[-v],Sin[u]bimbi[-v]-Exp[v]/2,Sin[v]+0.3},
{Cos[u]kozep[2v]/2,Sin[u]kozep[2v]/2,Sin[2v]Cos[2v]/2-0.5}
},{u,0,2π},{v,-π/2,0},PlotRange->2,  ColorFunction->Function[{x,y,z,u,v},Hue[-(z-1)(v+0.2)/2]],Boxed->False,Axes->None,Mesh->None]

A világ kitárul!

Animate[ParametricPlot3D[{
{Cos[u]/((-a)*v^3-1/(-a)*v^2-(-a)/2*v+a),Sin[u]/((-a)*v^3-1/(-a)*v^2-(-a)/2*v+a),v},
{Cos[u]bimbi[-v]+Exp[v]/a,Sin[u]bimbi[-v],Sin[v]+0.3},
{Cos[u]bimbi[-v]-Exp[v]/a,Sin[u]bimbi[-v],Sin[v]+0.3},
{Cos[u]bimbi[-v],Sin[u]bimbi[-v]+Exp[v]/a,Sin[v]+0.3},
{Cos[u]bimbi[-v],Sin[u]bimbi[-v]-Exp[v]/a,Sin[v]+0.3},
{-Cos[u]kozep[2v]/2/a,-Sin[u]kozep[2v]/2/a,-Sin[2v]Cos[2v]/a/2-0.5}
},{u,-2π,π},{v,-π/2,0}, PlotRange->2, ColorFunction->Function[{x,y,z,u,v},Hue[-(z-1)(v+0.2)/2]],Boxed->False,Axes->None,Mesh->None],{a,-2.5,-1},AnimationRunning->False]

Egy egyszerű tölcsér

r[x_]:=Exp[-2.5x^(1/2)]

ParametricPlot3D[{Cos[u]r[2v],Sin[u]r[2v],-2v},{u,0,2π},{v,-π/2,π/2}, PlotRange->2, PlotStyle->{Yellow,Specularity[Blue,2]},Axes->None,Mesh->None]

Megdöntve

ParametricPlot3D[{Cos[u]r[2v]+Exp[-2v],Sin[u]r[2v],-2v},{u,0,2π},{v,-π/2,π/2}, PlotRange->2, PlotStyle->{Yellow,Specularity[Blue,10]},Axes->None,Mesh->None]

ParametricPlot3D[{
{Cos[u] r[2v],Sin[u] r[2v],-2v},
{Cos[u] bimbi[v]+Exp[-2v],Sin[u] bimbi[v],-Sin[v]+0.5},
{Cos[u] bimbi[v]-Exp[-2v],Sin[u] bimbi[v],-Sin[v]+0.5},
{Cos[u] bimbi[v],Sin[u] bimbi[v]+Exp[-2v],-Sin[v]+0.5},
{Cos[u] bimbi[v],Sin[u] bimbi[v]-Exp[-2v],-Sin[v]+0.5}
},{u,0,2 π},{v,-π/2,π/2},PlotRange->1.5,ColorFunction->Function[{x,y,z,u,v},Hue[v/2]],Boxed->False,Axes->None,Mesh->None]

Színes virágcsokor

ParametricPlot3D[{
{Cos[u]r[2v]+1.5Exp[-2v],Sin[u]r[2v],-2v},
{Cos[u]r[2v]-1.5Exp[-2v],Sin[u]r[2v],-2v},
{Cos[u]r[2v],Sin[u]r[2v]+1.5Exp[-2v],-2v},
{Cos[u]r[2v],Sin[u]r[2v]-1.5Exp[-2v],-2v},
{Cos[u] bimbi[v]+1.5Exp[-v],Sin[u] bimbi[v],-Sin[v]},
{Cos[u] bimbi[v]-1.5Exp[-v],Sin[u] bimbi[v],-Sin[v]},
{Cos[u] bimbi[v],Sin[u] bimbi[v]+1.5Exp[-v],-Sin[v]},
{Cos[u] bimbi[v],Sin[u] bimbi[v]-1.5Exp[-v],-Sin[v]},
{2Cos[u] r[2v],2Sin[u] r[2v],-4v+1},
{2Cos[u] bimbi[v]+2Exp[-2v],2Sin[u] bimbi[v],-Sin[v]+1.5},
{2Cos[u] bimbi[v]-2Exp[-2v],2Sin[u] bimbi[v],-Sin[v]+1.5},
{2Cos[u] bimbi[v],2Sin[u] bimbi[v]+2Exp[-2v],-Sin[v]+1.5},
{2Cos[u] bimbi[v],2Sin[u] bimbi[v]-2Exp[-2v],-Sin[v]+1.5}
},{u,0,2π},{v,-π/2,π/2}, PlotRange->2.5, ColorFunction->Function[{x,y,z,u,v},Hue[v/2]],Boxed->False,Axes->None,Mesh->None]

Gombacsoport

ParametricPlot3D[{
{2Cos[u] r[v]+1.5Exp[-v]/2-0.5,2Sin[u] r[v],-2v+1},
{Cos[u]r[v]+2Exp[-v]-0.5,Sin[u]r[v],-v+0.2},
{Cos[u]r[v]-0.5,Sin[u]r[v]+1.5Exp[-v],-v},
{Cos[u]r[v]-0.5,Sin[u]r[v]-1.5Exp[-v],-v},
{Cos[u]r[v]/2+1.5Exp[-v]/2-0.5,Sin[u]r[v]/2+1.5Exp[-v]/2,-v-0.5},
{Cos[u]r[v]/2+1.5Exp[-v]/2-0.5,Sin[u]r[v]/2-1.5Exp[-v]/2,-v-0.5},
{2Cos[u]r[v]/3+4Exp[-v]/3-0.5,2Sin[u]r[v]/3+Exp[-v]/2,-v-0.7}
},{u,0,2π},{v,-π,π}, PlotRange->2.5, ColorFunction->"DarkRainbow",Boxed->False,Axes->None,Mesh->None]

Még

r2[x_]:=x^(1/2)

ParametricPlot3D[
{Cos[u]r2[2v],Sin[u]r2[2v],r2[2v]Sin[1.1v]/v/0.6-2},
{u,0,2π}, {v,-π/2,π/2},PlotRange->2,ColorFunction->Function[{x,y,z,u,v},Hue[-(z-1)(v+0.2)/2]],Axes->None,Mesh->None]

A levél

ParametricPlot3D[
{1.25Cos[u]r2[2v]*Sin[4u],1.25Sin[u]r2[2v]Sin[4u],Sin[4u]r2[2v]Sin[1.1v]/v-2},{u,0,2π}, {v,-π/2,π/2},PlotRange->2,ColorFunction->"AvocadoColors",Axes->None,Mesh->None]

ParametricPlot3D[{
{Cos[u]r2[2v]0.8,Sin[u]r2[2v]0.8,r2[2v]Sin[1.1v]/v/0.6-2},
{Cos[u]bimbi[v]+Exp[-v^2]/2-0.05,Sin[u]bimbi[v],-Sin[v]},
{Cos[u]bimbi[v]-Exp[-v^2]/2+0.05,Sin[u]bimbi[v],-Sin[v]},
{Cos[u]bimbi[v]+Exp[-v]-0.2,Sin[u]bimbi[v],-Sin[v]},
{Cos[u]bimbi[v]-Exp[-v]+0.2,Sin[u]bimbi[v],-Sin[v]},
{Cos[u]bimbi[v]+Exp[-v^2]/2-0.05,Sin[u]bimbi[v]+Exp[-v^2]/2-0.05,-Sin[v]},
{Cos[u]bimbi[v]-Exp[-v^2]/2+0.05,Sin[u]bimbi[v]-Exp[-v^2]/2+0.05,-Sin[v]},
{Cos[u]bimbi[v]+Exp[-v]-0.2,Sin[u]bimbi[v]+Exp[-v]-0.2,-Sin[v]},
{Cos[u]bimbi[v]-Exp[-v]+0.2,Sin[u]bimbi[v]-Exp[-v]+0.2,-Sin[v]},
{Cos[u]bimbi[v]-Exp[-v^2]/2+0.05,Sin[u]bimbi[v]+Exp[-v^2]/2-0.05,-Sin[v]},
{Cos[u]bimbi[v]+Exp[-v^2]/2-0.05,Sin[u]bimbi[v]-Exp[-v^2]/2+0.05,-Sin[v]},
{Cos[u]bimbi[v]-Exp[-v]+0.2,Sin[u]bimbi[v]+Exp[-v]-0.2,-Sin[v]},
{Cos[u]bimbi[v]+Exp[-v]-0.2,Sin[u]bimbi[v]-Exp[-v]+0.2,-Sin[v]},
{Cos[u]bimbi[v],Sin[u]bimbi[v]+Exp[-v^2]/2-0.05,-Sin[v]},
{Cos[u]bimbi[v],Sin[u]bimbi[v]-Exp[-v^2]/2+0.05,-Sin[v]},
{Cos[u]bimbi[v],Sin[u]bimbi[v]+Exp[-v]-0.2,-Sin[v]},
{Cos[u]bimbi[v],Sin[u]bimbi[v]-Exp[-v]+0.2,-Sin[v]},
{1.25Cos[u]r2[2v]*Sin[6u],1.25Sin[u]r2[2v]Sin[6u],Sin[6u]r2[2v]Sin[1.1v]/v-2}
},{u,0,2π}, {v,-π/2,π/2},PlotRange->2,ColorFunction->Function[{x,y,z,u,v},Hue[-(z-1)(v+0.3)/2]],Boxed->False,Axes->None,Mesh->None]

ParametricPlot3D[{
{Sin[4u+1]Cos[u]r2[2v-0.2],Sin[4u+1]Sin[u]r2[2v-0.2],r2[2v]Sin[1.1v]/v/0.6-2.7},
{Cos[u]bimbi[v]+Exp[-v^2]/2-0.05,Sin[u]bimbi[v],-Sin[v]-0.5},
{Cos[u]bimbi[v]-Exp[-v^2]/2+0.05,Sin[u]bimbi[v],-Sin[v]-0.5},
{Cos[u]bimbi[v]+Exp[-v]-0.2,Sin[u]bimbi[v],-Sin[v]-0.5},
{Cos[u]bimbi[v]-Exp[-v]+0.2,Sin[u]bimbi[v],-Sin[v]-0.5},
{Cos[u]bimbi[v]+Exp[-v^2]/2-0.05,Sin[u]bimbi[v]+Exp[-v^2]/2-0.05,-Sin[v]-0.5},
{Cos[u]bimbi[v]-Exp[-v^2]/2+0.05,Sin[u]bimbi[v]-Exp[-v^2]/2+0.05,-Sin[v]-0.5},
{Cos[u]bimbi[v]+Exp[-v]-0.2,Sin[u]bimbi[v]+Exp[-v]-0.2,-Sin[v]-0.5},
{Cos[u]bimbi[v]-Exp[-v]+0.2,Sin[u]bimbi[v]-Exp[-v]+0.2,-Sin[v]-0.5},
{Cos[u]bimbi[v]-Exp[-v^2]/2+0.05,Sin[u]bimbi[v]+Exp[-v^2]/2-0.05,-Sin[v]-0.5},
{Cos[u]bimbi[v]+Exp[-v^2]/2-0.05,Sin[u]bimbi[v]-Exp[-v^2]/2+0.05,-Sin[v]-0.5},
{Cos[u]bimbi[v]-Exp[-v]+0.2,Sin[u]bimbi[v]+Exp[-v]-0.2,-Sin[v]-0.5},
{Cos[u]bimbi[v]+Exp[-v]-0.2,Sin[u]bimbi[v]-Exp[-v]+0.2,-Sin[v]-0.5},
{Cos[u]bimbi[v],Sin[u]bimbi[v]+Exp[-v^2]/2-0.05,-Sin[v]-0.5},
{Cos[u]bimbi[v],Sin[u]bimbi[v]-Exp[-v^2]/2+0.05,-Sin[v]-0.5},
{Cos[u]bimbi[v],Sin[u]bimbi[v]+Exp[-v]-0.2,-Sin[v]-0.5},
{Cos[u]bimbi[v],Sin[u]bimbi[v]-Exp[-v]+0.2,-Sin[v]-0.5},
{1.5Cos[u]r2[2v]*Sin[6u],1.5Sin[u]r2[2v]Sin[6u],Sin[6u]r2[2v]Sin[1.1v]/v-2}
},{u,0,2π}, {v,-π/2,π/2},PlotRange->2,ColorFunction->"SunsetColors",Boxed->False,Axes->None,Mesh->None]

ParametricPlot3D[{
{Sin[4u]Cos[u]r2[v-0.5]0.8,0.8Sin[4u]Sin[u]r2[v-0.5],r2[v]Sin[0.55v]/v/0.3-2.5},
{1.25Cos[u]r2[v]*Sin[6u],1.25Sin[u]r2[v]Sin[6u],Sin[6u]r2[v]Sin[0.55v]/v/0.5-2},
{Cos[u]/15,Sin[u]/15,Log[v]/5-0.6},
{Cos[u]kozep[v]/10,Sin[u]kozep[v]/10,Sin[v]Cos[v]/8-0.4}
},{u,0,2π}, {v,-π,π},PlotRange->2,ColorFunction->Function[{x,y,z,u,v},Hue[-(z-1)(v+0.6)/2]],Boxed->False,Axes->None,Mesh->None]

A tölcsérből

ParametricPlot3D[{Cos[u]r[v-0.5]Sin[4u],Sin[u]r[v-0.5]Sin[4u],-v+1},{u,0,2π},{v,-π,π}, PlotRange->1, PlotStyle->{Yellow,Specularity[Pink,1]},Axes->None,Mesh->None]

ParametricPlot3D[{{Cos[u+π]r[v-0.5]Sin[4u],Sin[u+π]r[v-0.5]Sin[4u],Sin[u/4]4r[v]-1},
{Cos[u+π/3]r[v-0.5]Sin[4u],Sin[u+π/3]r[v-0.5]Sin[4u],Sin[u/4]4r[v]},
{Cos[u+2π/3]r[v-0.5]Sin[4u],Sin[u+2π/3]r[v-0.5]Sin[4u],Sin[u/4]4r[v]-0.5}},{u,0,2π},{v,-π,π}, PlotRange->1,PlotStyle->{Green, Red, Yellow},Boxed->False,Axes->None,Mesh->None]

ParametricPlot3D[{
{Cos[u+1/π]r[v-0.5]Sin[4u],Sin[u+1/π]r[v-0.5]Sin[4u],Sin[u/4]4r[v]-1},
{Cos[u+π]r[v-0.5]Sin[4u],Sin[u+π]r[v-0.5]Sin[4u],-v+1},
{Cos[u+2/π]r[v-0.5]Sin[4u],Sin[u+2/π]r[v-0.5]Sin[4u],Sin[u/4]4r[v]-0.5}
},{u,0,2π},{v,-π,π}, PlotRange->1,ColorFunction->"Rainbow",Boxed->False,Axes->None,Mesh->None]

r0[x_]:=1/(x^3-x^2-1/2x-1)

ParametricPlot3D[{
{Sin[4u]Cos[u+3/2/π]r0[2v],Sin[4u]Sin[u+3/2/π]r0[2v],2v},
{Cos[u]bimbi[-v]+Exp[v]/3,Sin[u]bimbi[-v],Sin[v]+0.2},
{Cos[u]bimbi[-v]-Exp[v]/3,Sin[u]bimbi[-v],Sin[v]+0.2},
{Cos[u]bimbi[-v],Sin[u]bimbi[-v]+Exp[v]/3,Sin[v]+0.2},
{Cos[u]bimbi[-v],Sin[u]bimbi[-v]-Exp[v]/3,Sin[v]+0.2},
{Cos[u]kozep[2v]/3,Sin[u]kozep[2v]/3,Sin[2v]Cos[2v]/3}
},{u,0,2π},{v,-π/2,0},PlotRange->2,ColorFunction->"Rainbow",ColorFunction->Function[{x,y,z,u,v},Hue[-(z-1)(v+0.2)/2]],Boxed->False,Axes->None,Mesh->None]

Animate[ParametricPlot3D[{
{Sin[4u]Cos[u+3/2/π]/((-a)*8v^3-1/(-a)*4v^2-(-a)*v+a),Sin[4u]Sin[u+3/2/π]/((-a)*8v^3-1/(-a)*4v^2-(-a)*v+a),2v},{Cos[u]bimbi[-v]+Exp[v]/a/2,Sin[u]bimbi[-v],Sin[v]+0.3},
{Cos[u]bimbi[-v]-Exp[v]/a/2,Sin[u]bimbi[-v],Sin[v]+0.3},
{Cos[u]bimbi[-v],Sin[u]bimbi[-v]+Exp[v]/2/a,Sin[v]+0.3},
{Cos[u]bimbi[-v],Sin[u]bimbi[-v]-Exp[v]/a/2,Sin[v]+0.3},
{-Cos[u]kozep[2v]/4/a,-Sin[u]kozep[2v]/4/a,-Sin[2v]Cos[2v]/a/4}
},{u,-2π,π},{v,-π/2,0}, PlotRange->2, ColorFunction->"Rainbow",ColorFunction->Function[{x,y,z,u,v},Hue[-(z-1)(v+0.2)/2]],Boxed->False,Axes->None,Mesh->None],{a,-2.5,-1},AnimationRunning->False]