Einfache Fraktale * Fractals simples

Komplexe Quadratfolgen * Suites quadratiques complexes

Remove["Global`*"];
z = 1 + I;
tab1 = Table[z^n, {n, 1, 5}];
tab2 = Table[(z/2)^n, {n, 1, 5}];
tab3 = 
        Table[(z/Sqrt[2])^n, {n, 1, 5}];
tab11 = 
        Table[{Re[tab1[[k]]], Im[tab1[[k]]]}, {k, 1, 
            Length[tab1]}];
tab21 = 
        Table[{Re[tab2[[k]]], Im[tab2[[k]]]}, {k, 1, 
            Length[tab2]}];
tab31 = 
        Table[{Re[tab3[[k]]], Im[tab3[[k]]]}, {k, 1, 
            Length[tab3]}];
p1 = Map[Point, tab11];
p2 = Map[Point, tab21];
p3 = Map[Point, tab31];
Show[
        Graphics[
          Join[Prepend[p1, PointSize[0.03]], Prepend[p2, PointSize[0.03]], 
            Prepend[p3, 
              PointSize[0.03]], {Circle[{0, 0}, 
                1], 
Line[{{-6, 0}, {2, 0}}], 
              Line[{{0, -4}, {0, 3}}]}]], 
        AspectRatio -> Automatic];
Join[
        Prepend[p1, 
          PointSize[
            0.03]], {Line[{{-6, 0}, {2, 
                0}}]}];

Fraktal iterativ programmiert * Fractal programmé de façon itérative

Remove["Global`*"];
la1 = 
      3000;     
p[0] = -1 + 
        I;
z[1] = 2 - I; z[2] = 4 + 2 I; z[3] = 3 - 2  I;  
    z[4] = 3  I;
f[n_] := Floor[4  Random[ ]] + 1;
tab1 = Table[f[n], {n, 1, la1}];
p[1] = (z[tab1[[1]]] + p[0])/
          2  ;
Do[
        p[n] = (z[tab1[[n]]] + p[n - 1])/2  , {n, 2, 
          la1}];
tab2 = Table[p[n], {n, 0, la1}] // N;
tab3 = 
        Table[{Re[tab2[[k]]], Im[tab2[[k]]]}, {k, 1, 
            Length[tab2]}];
po = Map[Point, tab3];
tab4 = {z[1], z[2], z[3], z[4]};
tab5 = 
        Table[{Re[tab4[[k]]], Im[tab4[[k]]]}, {k, 1, 
            Length[tab4]}];
po1 = Map[Point, tab5];
Show[
        Graphics[
          Join[Prepend[po, PointSize[0.02]], 
            Prepend[po1, 
              PointSize[
                0.05]], 
Prepend[{Point[{Re[p[0]], 
                    Im[p[0]]}]}, 
              PointSize[0.07]], {Circle[{0, 0}, 
                1], 
Line[{{-5, 0}, {5, 0}}], 
              Line[{{0, -2.2}, {0, 4}}]}]], 
        AspectRatio -> Automatic];

Fraktal rekursiv programmiert * Fractal programmé de façon récursive

Remove["Global`*"];
la1 = 
      253;     
p[0] = -1 + 
        I;
z[1] = 2 - I; z[2] = 4 + 2 I; z[3] = 3 - 2  I;  
    z[4] = 3  I;
f[n_] := Floor[4  Random[ ]] + 1;
tab1 = Table[f[n], {n, 1, la1}];
p[1] = (z[tab1[[1]]] + p[0])/
          2  ;
p[n_] := (z[tab1[[n]]] + p[n - 1])/
          2  ;
tab2 = Table[p[n], {n, 0, la1}] // N;
tab3 = 
        Table[{Re[tab2[[k]]], Im[tab2[[k]]]}, {k, 1, 
            Length[tab2]}];
po = Map[Point, tab3];
Show[
        Graphics[
          Join[Prepend[po, 
              PointSize[0.02]], {Circle[{0, 0}, 
                1], 
Line[{{-5, 0}, {5, 0}}], 
              Line[{{0, -4}, {0, 4}}]}]], 
        AspectRatio -> Automatic];

Work

Remove["Global`*"];