(*Mathematica code for drawing a square grid*)plotgrid2[data_]:=(J=Length[data];
K=Length[data[[1]]];
lines={};
Do[Do[AppendTo[lines,Graphics[Line[{{Re[data[[j,k]]],Im[data[[j,k]]]},{Re[data[[j,k+1]]],Im[data[[j,k+1]]]}}]]];,{j,1,J}];,{k,1,K-1}];
Do[Do[AppendTo[lines,Graphics[Line[{{Re[data[[j,k]]],Im[data[[j,k]]]},{Re[data[[j+1,k]]],Im[data[[j+1,k]]]}}]]];,{j,1,J-1}];,{k,1,K}];
Show[{lines},AspectRatio->Automatic,Axes->Automatic,PlotRange->All]);

grid1=Table[(1/10)(j+I k),{j,0,20},{k,0,20}];
grid2=Table[(1/10)(j+I k),{j,0,20},{k,0,61}];

plotgrid2[grid1]

plotgrid2[grid1^2]

plotgrid2[grid1^(1/2)]

Manipulate[plotgrid2[grid1^t],{t,.1,4}];