Work Animations

1 Planeten

Remove["Global`*"]

?PlotRegion

Options[Plot3D]

r=0.7;m=50;
x1[k_]:= 4 Cos[k 2 Pi/m]+1;
y1[k_]:= 4 Sin[k 2 Pi/m];
x2[k_]:= 4 Cos[k 2 Pi/m+Pi]+1;
z2[k_]:= 4 Sin[k 2 Pi/m];

<<Graphics`Polyhedra`;
Show[
    Polyhedron[GreatStellatedDodecahedron],
    Polyhedron[Icosahedron, {3, 3, 3}, r],
    Polyhedron[ Dodecahedron, {-3, 3, 3}, r],
    Boxed->False,PlotRegion->{{0.1,0.8},{0.1,0.8}}];

st=Table[Show[
    Polyhedron[GreatStellatedDodecahedron],
    Polyhedron[Icosahedron, {x1[k], y1[k], 0}, r],
    Polyhedron[ Dodecahedron, {x2[k],0,z2[k]}, r],
    Boxed->False,PlotRegion->{{0.1,0.8},{0.1,0.8}},
    ViewPoint->{-2.722 Cos[k Pi/m], -Sin[k Pi/m], 3 (1+Sin[k]^2)}],
    {k,1,2m}];

Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationPlaneten",st,"GIF"]

2 Tanz

Remove["Global`*"]

f[x_] := x;
f[x_ /; x > 1] := Floor[x];
g[x_] := f[Mod[x, 2]] + Floor[x/2];
h[t_, n_] := 
        Pi g[n 2  t/Pi]/2 /n;
s[t_, n_] := t n  Pi;

parP[k_]:=ParametricPlot[{Cos[h[t,k]],Sin[h[t,k]]} (3+Sin[2 t k]),{t,0,4Pi},
      AspectRatio->Automatic,PlotRange->All,DisplayFunction->Identity,PlotPoints->40];
      parP1[k_]:=ParametricPlot[{Cos[h[t,k]+Pi/8],Sin[h[t,k]+Pi/8]} (3-Sin[2 t k]^2),{t,0,4Pi},AspectRatio->Automatic,PlotRange->All,DisplayFunction->Identity,PlotPoints->40];
pt1[k_]:={Cos[h[t,k]],Sin[h[t,k]]} (3+Sin[2 t k]);
pt2[k_]:={Cos[h[t,k]+Pi/8],Sin[h[t,k]+Pi/8]} (3-Sin[2 t k]^2);

tabFilm[k_, r_] := 
        Table[Show[parP[k], parP1[k], 
            Graphics[{Circle[{0, 0}, r], Circle[{0, 0}, r + 1.5], Hue[0.6], 
                PointSize[0.06], Point[pt1[k]], Hue[1], Point[pt2[k]]}], 
            AspectRatio -> Automatic, PlotRange -> All, 
            DisplayFunction -> $DisplayFunction, 
            PlotRegion -> {{0.3, 0.8}, {0.3, 0.8}}], {t, 0, 4 Pi, 
            0.1}];
tabFilm[2, 3];

Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationTanz",tabFilm[2,3],"GIF"]

3 1. Saite

Remove["Global`*"]

a=0.5;aA=1;ω=2;
y[x_,t_]:=Which[t≥x/a, aA Sin[ω(t-x/a)]+1,t<x/a,0];
ani1=Table[
      Plot[{y[x,t],0,2},{x,0,1},PlotRange->{0,2},Ticks->False,
        AxesOrigin->{0,0},PlotStyle->{Thickness[.02]},PlotRegion->{{0.1,0.8},{0.1,0.8}}],{t,0,2N[Pi],2N[Pi]/40.}];
        
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationSaite1",ani1,"GIF"]

3 2. Saite

Remove["Global`*"]

f[t_,c_]:=(Sin[t]Sin[c]+Sin[2t]/3 Sin[2c]+Sin[3t]/5 Sin[3c]+Sin[4t]/7 Sin[4c]+Sin[6t]/9 Sin[5c]);
ani2=Table[
      Plot[f[t,c],{t,0,2Pi},PlotRange->{-1.5,1.5},Ticks->False,PlotRegion->{{0.1,0.8},{0.1,0.8}}],{c,
        0,4Pi,2Pi/4 0.1}];
        Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationSaite",ani2,"GIF"]

4. Schnecke

Remove["Global`*"];

vX[t_]:= 3  Sin[t 2Pi/m];
vY[t_]:= 2 Cos[t 2Pi/m];
vZ[t_]:= 3  Cos[t 2Pi/m];
viewP[t_]:=Evaluate[ {vX[t],vY[t],vY[t]}];

druck[t_]:=ParametricPlot3D[{u Cos[u](4+Cos[v+u]),u Sin[u](4+Cos[v+u]),u Sin[v+u]},{u,0,4Pi},{v,0,2Pi},PlotPoints->{60,12},ViewPoint->viewP[t],Axes->False,Boxed->False,PlotRegion->{{0,1},{0,1}},DisplayFunction:>Identity,PlotRegion->{{0.1,0.8},{0.1,0.8}}];
m=40;
ani=Table[Show[druck[t],DisplayFunction:>$DisplayFunction],{t,1,m}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationSchnecke",ani,"GIF"]

5. Tanz der Hülle (Ostschweizerin)

Remove["Global`*"];
f[x_] := Re[Sqrt[44^2 - x^2]/2]; 
    g[x_, y_] := 
      Re[Sqrt[44^2 - 
              4 ( x - 22)^2 - (y + 44)^2] (y/
                88)^2];
h[x_, y_] := 
        Re[Sqrt[44^2 - 
                4 ( x + 22)^2 - (y + 44)^2] (y/
                  88)^2];
k[x_, y_] := 
      Re[Sqrt[30 -  ( x - 22)^2 - (y + 74)^2] /5  + 
          Sqrt[10 - (x - 22)^2 - (y + 74)^2]]; 
    l[x_, y_] := 
      Re[Sqrt[30 -  ( x + 22)^2 - (y + 74)^2] /5  + 
          Sqrt[10 - (x + 22)^2 - (y + 
                    74)^2]];
z[x_, y_] := 
        f[x] + g[x, y] + h[x, y] + k[x, y] + 
          l[x, y];
vX[t_] :=  3  Sin[t 2  Pi/m];
vY[t_] :=  4 Cos[t 2  Pi/m];
vZ[t_] :=  3  Sin[t 2  Pi/m];
viewP[t_] := 
        Evaluate[ {vX[t], vY[t], vY[t]}];
druck[t_] := 
        Plot3D[z[(Sin[t 2  Pi/m] + 4)^2 x/4, y], {x, -44, 
            44}, {y, -95, 0}, PlotPoints -> 100, 
          ViewVertical -> {0, 1, 0}, ViewPoint -> viewP[t], 
          Axes -> False, 
          Boxed -> False,    
          PlotRegion -> {{0.1, 1}, {0.1, 1}}, 
          DisplayFunction :> 
            Identity];
m = 40;
ani = 
        Table[Show[druck[t], 
            DisplayFunction :> $DisplayFunction], {t, 1, 
            m}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/\
Animationen/GIFAnimationTanzDerHuelle", ani, "GIF"]

6. Brezel3D

Vorspann

Seitenansicht

Remove["Global`*"]

r[t_] :=  Cos[3  t]; 
x[t_] :=  r[t] Sin[t];  
y[t_] :=  r[t] Cos[t];  
f[t_] := {x[t], y[t]};
ParametricPlot[f[t], {t, 0, 2 Pi}, Ticks -> False, 
        AspectRatio -> Automatic];

Zentrum öffnen

r[t_] :=  1 + 1/3 Cos[3/2 t]; 
x[t_] :=  r[t] Sin[t];  
y[t_] :=  r[t] Cos[t];  
f[t_] := {x[t], y[t]};
ParametricPlot[f[t], {t, 0, 4 Pi}, Ticks -> False, 
        AspectRatio -> Automatic];

Uebertragung in 3D

r[t_] :=  1 + 1/3 Cos[3/2 t]; 
x[t_] :=  r[t] Sin[t];  
y[t_] :=  r[t] Cos[t];  
z[t_] := 0.6  Sin[3/2 t];  
f[t_] := {x[t], y[t], z[t]};
ParametricPlot3D[f[t], {t, 0, 4 Pi}, Ticks -> False, 
        PlotRange -> All, AxesLabel -> {x, y, z}, 
        AspectRatio -> Automatic];

Mantel erstellen

vLen[v_] := Sqrt[v . v]; 
normVec[v_] := v/vLen[v];
getVect90[v_] := {-v[[2]], v[[1]], 
        0}
vT[t_] = normVec[f'[t]];
vN[t_] = normVec[getVect90[vT[t]]];
vB[t_] := Cross[vT[t], vN [t]];

mantel[t_, u_, r_] := 
        f[t] + r (vN[t] Cos[u] + vB[t] Sin[u]);

Graphic

myPlot = 
        ParametricPlot3D[
          Evaluate[mantel[t, u, 0.3]], {t, 0, 4  Pi}, {u, 0, 2  Pi}, 
          PlotRange -> All, AxesLabel -> {x, y, z}, 
          AspectRatio -> Automatic, Axes -> False, Boxed -> False, 
          PlotPoints -> 40];

myPlot = 
        ParametricPlot3D[
          Evaluate[mantel[t, u, 0.1]], {t, 0, 4  Pi}, {u, 0, 2  Pi}, 
          PlotRange -> All, AxesLabel -> {x, y, z}, 
          AspectRatio -> Automatic, Axes -> False, Boxed -> False, 
          PlotPoints -> 60];

Animation

Es esistieren diverse Animationsmethoden. Da nicht immer alles geht, probieren wir:

Do[Plot[Sin[n x], {x, 0, 2  π}], {n, 1, 3, 0.25}];

nn = 10; While[(nn = nn - 1) > 5, Print[nn]]

Animation mit dem 3D-Brezel:

pPl[r1_] := 
        ParametricPlot3D[
          Evaluate[mantel[t, u, r1]], {t, 0, 4  Pi}, {u, 0, 2  Pi}, 
          Boxed -> False, Axes -> False, 
          PlotRegion -> {{0.1, 0.8}, {0.1, 0.8}}];

pPl[0.1];

ani = 
        Table[Show[pPl[nn/20], 
            DisplayFunction :> $DisplayFunction], {nn, 20, 
            1, -1}];

    Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/\
GIFAnimationBrezelkrampf", ani, "GIF"]

Nochmals

mNew=50;kkk=5;
ParametricPlot3D[Evaluate[mantel[t,u,0.1]],{t,0,4Pi},{u,0,2Pi},Boxed->False,Axes->False];
ParametricPlot3D[Evaluate[mantel[t,u,0.1]],{t,0,4Pi},{u,0,2Pi},Boxed->False,Axes->False,
ViewPoint->{-2.722 Cos[kkk Pi/mNew], -Sin[kkk Pi/mNew], 3 (1+Sin[kkk]^2)}];

?AxesOrigin

mNew=50;kkk=.;
pPlV[kkk_]:=ParametricPlot3D[Evaluate[mantel[t,u,0.1]],{t,0,4Pi},{u,0,2Pi},Boxed->False,Axes->False,
ViewPoint->{-2 Cos[kkk Pi/mNew], -2 Sin[kkk Pi/mNew], 2},DisplayFunction:>Identity,PlotRegion->{{0.1,0.8},{0.1,0.8}}];
pPlV[5];

ani=Table[
      Show[Evaluate[pPlV[kkk]],DisplayFunction:>$DisplayFunction],{kkk,1,2}];

ani=Table[
      Show[Evaluate[pPlV[kkk]],DisplayFunction:>$DisplayFunction],{kkk,1,mNew}];
      Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/\
GIFAnimationBrezelflug",ani,"GIF"]

Options[ParametricPlot]

7. Insektenflug

Remove["Global`*"];
f[α_, r0_, t_, t0_] := r0 E^(Tan[α] (t - t0));  
    step = 30; a = Table[Random[Real, {-Pi/4, Pi/4}], {j, 1, step}] ; 
    tt = Table[
        Random[Real, {0, 3}], {j, 1, step}] ;
rs = 5;  q3 = 1; t0 = 0; r = step;  
    z = Array[p, step - 1];
For[i = 1, 
        i ≤ step - 1, i++, 
If[
          Abs[f[a[[i]], rs, Sum[tt[[j]], {j, 1, i}], t0]*q3] <= 0.5, 
          ex = 1; msg = "Insekt hat Pech", ex = 0; 
          msg = "Insekt hat Glück"]; 
p[
            i] = ParametricPlot[{Cos[t], Sin[t]} f[a[[i]], rs, t, t0]*
              q3, {t, Sum[tt[[j]], {j, 1, i - 1}], 
              Sum[tt[[j]], {j, 1, i}]}, DisplayFunction -> Identity, 
            Axes -> False, 
            PlotRegion -> {{0, 1}, {0, 1}}]; 
Append[
          z, p[i]]; 
q3 = (Abs[
                f[a[[i]], rs, Sum[tt[[j]], {j, 1, i}], t0]*
                  q3])/(Abs[
                f[a[[i + 1]], rs, Sum[tt[[j]], {j, 1, i}], 
                  t0]]); 
If[ex == 1, r = i;  
          i = step;, r = i;];];
ani = 
        Table[Show[Take[z, h], 
            Graphics[
              Disk[{0, 0}, 
                0.5]], {DisplayFunction -> $DisplayFunction}]  , {h, 1, r}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/\
Animationen/GIFAnimationInsektenflug9", ani, "GIF"]

7. Berechnung von Krümmung und Anschmiegekreis bei ebenen Kurven

Definition der Raumkurve

Remove["Global`*"]

x[t_] := 0.5 t Cos[t];   y[t_] :=  t Sin[t];   z[t_] := 
      t;    v[t_] := {x[t], y[t], z[t]};

Definition des Bereiches der Variablen

tmin = 0.1;   tmax =  10;

Plot Ausgangsfunktion

origPlot = 
        ParametricPlot3D[
          Evaluate[Join[v[t],  {RGBColor[1, 0, 0]}]], {t, tmin, tmax}, 
          PlotRange -> All, AxesLabel -> {x, y, z}, 
          AspectRatio -> Automatic];

Begleitendes Dreibein

vLen[v_] := Sqrt[v . v]; 
normVec[v_] := v/vLen[v];
tg[t_] = normVec[v'[t]];
n[t_] = 
        normVec[Cross[
            Cross[v'[t], v''[t]], v'[
              t]]];
b[t_] := Cross[tg[t], n [t]];

{tg[t], n[t], b[t]}

tVec[t_] := 
        Line[{v[t], v[t] + 3  tg[t]}];
nVec[t_] := 
        Line[{v[t], v[t] + 3  n[t]}];
bVec[t_] := Line[{v[t], v[t] + 3  b[t]}];

dreibein[t_] := 
      Graphics3D[{RGBColor[1, 0, 1], tVec[t], RGBColor[0.01, 0.6, 0.62], 
          nVec[t], RGBColor[0.54, 0.17, 0.89], bVec[t]}]

Show[origPlot, dreibein[5]];

Krümmung

ϰ[t_] = 
        Sqrt[(((v''[t] . v''[t])*(v'[t] . v'[
                          t]) - (v''[t] . v'[t])^2)/
              vLen[v'[t]]^6)];
ϰ[t]

Plot[Evaluate[ϰ[t]], {t, tmin, tmax}];

Krümmungsradius

ρ[t_] := Abs[1/ϰ[t]];   ρ[t]

Plot[Evaluate[ρ[t]], {t, tmin, tmax}];

Krümmungskreismittelpunkt (Evolute)

m[t_] := v[t] +  ρ[t]*n[t];   m[t]

evolute = 
        ParametricPlot3D[
          Evaluate[Join[m[t], {RGBColor[0, 0, 1]}]], {t, tmin, tmax}, 
          PlotRange -> All, AspectRatio -> Automatic];

Schmiegekreis

myCirc3d[t_, k_] :=  
      m[t] +  ρ[t] (n[t] Cos[k] + tg[t] Sin[k]);   myCirc3d[t, 
      k]

Plot

circPlot[t_] := 
        ParametricPlot3D[
          Evaluate[Join[myCirc3d[t, k], {RGBColor[0, 1, 0]}]], {k, 0, 2 Pi}, 
          DisplayFunction -> Identity];

Show[origPlot, circPlot[6]];

Alles zusammen

Show[origPlot, circPlot[6], dreibein[6]];

Animation

zentrum[t_] := 
      Graphics3D[{RGBColor[1, 0.8, 0], PointSize[0.02], Point[m[t]] }];  
    zentrum[t]

ani = 
        Table[Show[evolute, origPlot, circPlot[s], zentrum[s], dreibein[s], 
            DisplayFunction -> $DisplayFunction,  
            AspectRatio -> Automatic, 
            PlotRange -> {{-15, 15}, {-12, 12}, {-1, 12}}, 
            AxesLabel -> {x, y, z}], {s, tmin, tmax, 
            0.2}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/\
Animationen/GIFAnimationRaumkurvenkrumm", ani, "GIF"]

8. Hüte

ani=Table[Plot3D[Re[E^-(0.3(x^2+y^2))Cos[1.5(x^2+y^2)+t]],{x,-3,3},{y,-3,3},PlotPoints->100,Mesh->False,Boxed->False,Axes->False,PlotRegion->{{0.1,1},{0.1,1}}],{t,0,Pi,Pi/15}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/\
GIFAnimationHuete",ani,"GIF"]

9. Kohler-Blume

h1  = ((100 - 7.1^2) (7.1^2 - 49))^(1/8)

Plot[((100 - r^2) (r^2 - 49))^(1/8), {r, 7.1, 
          9.6}];

VRx  := r Cos[φ];
VRy :=  r Sin[φ];
VRz  :=  
        17 - h1 + ((100 - r^2) (r^2 - 49))^(1/
                8);
p2  = 
        ParametricPlot3D[{VRx, VRy, 
            VRz, {EdgeForm[], SurfaceColor[RGBColor[1, 1, 1]]}}, {r, 7.1, 
            9.6}, {φ, 0, 2  Pi}, 
          PlotPoints -> 80];

Sx  :=  (4  Sin[x]) (0.4  Sin[y/3] + 
              2);
Sy  :=  (4  Cos[x]) (0.4  Sin[y/3] + 
              2);
Sz  :=   y;
p3  = 
        ParametricPlot3D[{Sx, Sy, 
            Sz, {EdgeForm[], SurfaceColor[RGBColor[1, 1, 1]]}}, {x, 0, 
            2 Pi}, {y, 0, 17}, PlotPoints  ->  80];

p5  = 
        ParametricPlot3D[{1.05  y Sin[x], 1.05  y Cos[x], 
            16 + 0.3  Sin[4  y], {EdgeForm[], 
              SurfaceColor[RGBColor[0.5, 0.3, 0]]}}, {x, 0, 2  Pi}, {y, 0, 
            2  Pi}, PlotPoints ->  80];

Stx  :=  
        Sqrt[y] + (Sin[x]) (0.2 Sin[y/2] + 
                1);
Sty  :=  
        Sqrt[y] + (Cos[x]) (0.2 Sin[y/2] + 
                1);
Stz  :=  16 + y;
p1  = 
        ParametricPlot3D[{Stx, Sty, 
            Stz, {EdgeForm[], SurfaceColor[RGBColor[0, 1, 0]]}}, {x, 0, 
            2 Pi}, {y, 0, 20}, PlotPoints  ->  80];

aZ  :=  11;
Vx  :=  4.4;
Vy  :=  4.4;
Sxy  :=  0.8;
Et  :=  6;
p4  =  
        ParametricPlot3D[{Vx + y Cos[x] (Et + Cos[aZ x]), 
            Vy + y (Et + Cos[aZ x]) Sin[x], 
            36 +  y^7,  {EdgeForm[], SurfaceColor[RGBColor[0, 1, 0]]}}, {x, 
            0, 2 Pi}, {y, 0, 1.1}, PlotPoints  ->  80];

aZ  :=  5;
Vx  :=  4.4;
Vy  :=  4.4;
Sxy  :=  1;
Et  :=  4;
p7  =  
        ParametricPlot3D[{Vx + y Cos[x] (Et + Cos[aZ x]), 
            Vy + y (Et + Cos[aZ x]) Sin[x], 
            36 +  y^7,  {EdgeForm[], SurfaceColor[RGBColor[1, 1, 0]]}}, {x, 
            0, 2 Pi}, {y, 1.1, 0}, PlotPoints  ->  80];

FBSx  :=  (1/y) ( Sin[x]) + 
          4.4;
FBSy  :=  (1/y ) (Cos[x]) + 
          4.4;
p6  = 
        ParametricPlot3D[{FBSx, FBSy, 
            38 + 3  Sin[y], {EdgeForm[], 
              SurfaceColor[RGBColor[0.8, 0, 0]]}}, {x, 0, 2 Pi}, {y, 0.3, 
            15}, PlotPoints ->  100];

plOut[t_] := 
        Show[{p1, p2, p3, p4, p5, p6, p7}, AspectRatio  -> Automatic,  
          Boxed -> False, Axes -> False, 
          ViewPoint -> {-5,  -10, 6 (1.5 - 1.7 Sin[t])}, 
          PlotRegion -> {{0.1, 0.8}, {0.1, 
                0.8}}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/\
Animationen/GIFAnimationKohlerBlume", 
      Table[plOut[t], {t, 0, Pi, 
          Pi/15}], "GIF"]

10. Parmameteränderung

Remove["Global`*"]

ani=Table[
      Plot[{x^2+b x+1},{x,-3,3},Ticks->False,
        AxesOrigin->{0,0},PlotStyle->{Thickness[.02]},PlotRegion->{{0.1,0.8},{0.1,0.8}},Epilog->{PointSize[0.05],Hue[1],Point[{-b/2, (-b/2)^2+b (-b/2)+1}]}],{b,-3,3,0.5}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationParabel",ani,"GIF"]

11. Ball

ani=Table[
      Plot[0,{x,0,2},PlotRange->{-0.03,4.5},Ticks->False,
        AxesOrigin->{0,0},PlotStyle->{Thickness[.02]},PlotRegion->{{0.1,0.8},{0.1,0.8}},Epilog->{PointSize[0.08],Hue[1],Point[{1,4-b^2}]}],{b,-2,2,0.25}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationBall",ani,"GIF"]

12. ImplicitPlot

Remove["Global`*"]

<< Graphics`ImplicitPlot`

imp[t_]:=ImplicitPlot[{(x^2 + t y^2)^2-(x^2 - y^2)+t x^2 y^3 == 0,
 (x^2 + t y^2)^2-2 x y == 0}, {x,-2,2},Ticks->False,
        AxesOrigin->{0,0},
PlotStyle->{Thickness[.02],Dashing[{.03}]},Epilog->{PointSize[0.08],Hue[1],Point[{0,0}]},PlotRegion->{{0.1,0.8},{0.1,0.8}}];
ani=Table[imp[t],{t,-2,2,0.2}];
Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationImplicit",ani,"GIF"]

12a. ....

12a. Farbvariationen

Options[Plot]

?Background

Remove["Global`*"];
m=60;
pS[t_]:=1/m+1-(t/m);
h1[t_]:=Abs[Sin[1. t]];
h2[t_]:=Abs[Sin[2. t]];
h3[t_]:=Abs[Sin[3. t]];
v[t_]:={1,1}+0.7 {Cos[t],Sin[t]}+0.3{Cos[6t],Sin[6t]};

p[t_]:=Plot[0,{x,0,2},
PlotRange->{-0.0,2},
Ticks->False,
AxesOrigin->{0,0},
(*PlotStyle->{Thickness[.01]},*)
Axes->False,
AspectRatio->Automatic,
PlotRegion->{{0.2,0.8},{0.2,0.8}},
Background->GrayLevel[Sin[(21- t/m)Pi]],
Epilog->
    Table[{Line[{{0,0},{2,0},{2,2},{0,2},{0,0}}],
PointSize[pS[t]],
RGBColor[h1[u],h2[u],h3[u]]/.u->s,
Point[v[s]]},{s,1,t}
     ]];
(* gAll[0]={};
gAll[t_]:=Append[gAll[0],Show[p[t]]];
gAll[s_]:=Table[p[t],{t,1,s}];*)
ani=Table[p[t],{t,1,m}
      ];
      Export["C:/EigeneFileWorkTansfer/HTAFilesTransfer/MathemDF/Animationen/GIFAnimationFarb",ani,"GIF"]