Pierwsze laboratoria z modelowania 14- 16

Jak sformatować rysunek?

Plot[Sin[x],{x,0,6Pi},PlotStyle->Directive[Thick,Pink], GridLines->Automatic,Frame->True,FrameStyle->Directive[14,Thick],FrameLabel->{"jedna oś","druga oś"}]

π ρ

(Sqrt[\[Placeholder]])

(Sqrt[2])

(1/4)

(2^10)

Deklarowanie zmiennych

Fun[x_,c_]:=c (x^2)

Fun[x,2]

?Fun

f1[n_]:=RandomReal[{0,1},5]
f2[n_]=RandomReal[{0,1},{5}]

f1[5]
f2[5]

Table[i^2,{i,5,100,5}]

Przechodzimy do instrukcji:

Mod[7,2π]//N

f[θ_,x_]:=Mod[x+θ,2π]

f[3,4]

Plot[f[1,x],{x,0,2π}]

Manipulate[Plot[f[a,x],{x,0,2π}],{{a,1},0,6}]

x0=0.5;
t0=4;
ListPlot[{x0,f[t0,x0],f[t0,f[t0,x0]],f[t0,f[t0,f[t0,x0]]]}]

x0=0.5;
t0=4;
{ListPlot[{x0,f[t0,x0],f[t0,f[t0,x0]],f[t0,f[t0,f[t0,x0]]]}],
Plot[f[1,x],{x,0,2π}]}

x0=0.5;
t0=4;
GraphicsGrid[{{ListPlot[{x0,f[t0,x0],f[t0,f[t0,x0]],f[t0,f[t0,f[t0,x0]]]}],
Plot[f[1,x],{x,0,2π}]}}]

{ListPlot[{x0,f[t0,x0],f[t0,f[t0,x0]],f[t0,f[t0,f[t0,x0]]]}],Plot[f[t0 k,x0],{k,0,2π}]}

Show[{ListPlot[{x0,f[t0,x0],f[t0,f[t0,x0]],f[t0,f[t0,f[t0,x0]]]}],Plot[f[t0 k,x0],{k,0,2π}]}]

Nest[f,x0,3]

?f

Nest[f[t0,#]&,x0,50]

NestList[f[t0,#]&,x0,50]

x0=0.5;
t0=3/4π;
ListPlot[NestList[f[t0,#]&,x0,200],Joined->True]

x0=0.5;
t0=3/4;
ListPlot[NestList[f[t0,#]&,x0,200],Joined->True]
ListPlot[NestList[f[t0,#]&,x0,200],Joined->False]

x0=0.5;
t0=3/4;
Histogram[NestList[f[t0,#]&,x0,2000],{0.05}]

x0=0.5;
t0=3/4π;
Histogram[NestList[f[t0,#]&,x0,2000],{0.05}]

Manipulate[Histogram[NestList[f[t0,#]&,x0,2000],{0.05}],{{x0,1},0,2π},{{t0,1},0,2π}]