f[λ_, x_]:= λ x(1-x)

?NestList

NestList[f[1.1,#]&, 0.3, 29]

ListPlot[NestList[f[1.1,#]&, 0.3, 29]]

Manipulate[ListPlot[NestList[f[λ, #]&, x, n], PlotRange -> {{0, All}, {0,1}}], {x, 0, 1}, {λ, 1, 4}, {n, 10, 100,1}]

ntaiteracja [λ_, x_, n_] := Nest[f[λ, #]&, x, n]

Plot[ntaiteracja[3.5, x,2], {x,0,1}]

Manipulate[Plot[{ntaiteracja[λ, x,n],x}, {x,0,1}, PlotRange -> {{0,All}, {0,1}}], {λ, 1,4}, {n,1,20,1}]

?Join

ListPlot[NestList[f[1.1,#]&, 0.3, 29], Joined-> True]

Zad. 6

x0 = RandomReal[];

?RandomReal

asymptot1[λ_, n_]:= NestList[f[λ,#]&, x0, n-1]

asymptot1[1,10]

n0

NestList[f[2,#]&, x0, 10-1]

asymptot2[λ_, n_, n0_]:= Take[NestList[f[λ,#]&, x0, n],-(n-n0)]

?f

asymptot[λ_, nn_Integer]:= NestList[f[λ,#]&, 0.2, nn]

ClearAll[asymptot2]

asymptot2[2, 10, 8]

?Riffle

asymptot3[λ_, n_, n0_] := Riffle[ConstantArray[λ, n-n0], Take[NestList[f[λ,#]&, x0, n],-(n-n0)]]

asymptot3[2, 10, 8]

asymptot4[λ_, n_, n0_]:= Table[asymptot3[λ, n, n0] , {λ,1,4,1}]

diagrambif[x0_, n_, n0_, krok_] := ListPlot[Partition[Flatten[Table[asymptot3[λ, n, n0] , {λ,1,4,0.01}]],2]]

diagrambif[x0, 400, 390, 0.01]