SetDirectory[NotebookDirectory[]];
Delta=1;L=50;N0=1000;Deltax=Deltay=Delta;nlast=1000;

For[k=1,k≤N0,k++,
x[k]=0;
y[k]=0;
];(*end for k*)
P[0]=Table[{x[k],y[k]},{k,1,N0}];
ListPlot[P[0],AspectRatio->1,GridLines->Automatic];

For[n=1,n≤nlast,n++,
For[k=1,k≤N0,k++,
q=Random[];
If[q≤0.25,x[k]=x[k]-Delta];
If[0.25<q≤0.5,x[k]=x[k]+Delta];
If[0.5<q≤0.75,y[k]=y[k]+Delta];
If[0.75<q≤1.0,y[k]=y[k]-Delta];
];(*end for k*)
P[n]=Table[{x[k],y[k]},{k,1,N0}];
];(*n*)

Manipulate[
ListPlot[P[n],AspectRatio->1,PlotRange->{{-L,L},{-L,L}},GridLines->Automatic],{n,0,nlast,1}
](*end Manipulate*)