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plotting - How can I improve my code for visualizing a complex map?


This code visualize a complex map, but it looks rather cumbersome:


F[z_] := z^2;
t1 = 0; 

t2 = Pi/3;
r1 = 1;
r2 = 3;
dt = (t2 - t1)/10;
dr = (r2 - r1)/10;

p1 = Show[
  Table[ParametricPlot[ReIm[r Exp[I t]], {r, r1, r2}], {t, t1, t2, 
    dt}],
  Table[ParametricPlot[ReIm[r Exp[I t]], {t, t1, t2}], {r, r1, r2, 

    dr}],
  ParametricPlot[ReIm[r Exp[I 4 dt]], {r, r1 + 5 dr, r1 + 6 dr}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[ReIm[r Exp[I 5 dt]], {r, r1 + 5 dr, r1 + 6 dr}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[ReIm[r Exp[I 6 dt]], {r, r1 + 6 dr, r1 + 7 dr}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[ReIm[r Exp[I 3 dt]], {r, r1 + 6 dr, r1 + 7 dr}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[

   ReIm[(r1 + 7 dr) Exp[I t]], {t, t1 + 3 dt, t1 + 6 dt}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[
   ReIm[(r1 + 6 dr) Exp[I t]], {t, t1 + 3 dt, t1 + 4 dt}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[
   ReIm[(r1 + 6 dr) Exp[I t]], {t, t1 + 5 dt, t1 + 6 dt}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[
   ReIm[(r1 + 5 dr) Exp[I t]], {t, t1 + 4 dt, t1 + 5 dt}, 

   PlotStyle -> {Black, Thickness[0.01]}],
  Axes -> None, PlotRange -> All]

p2 = Show[
  Table[ParametricPlot[ReIm[F[r Exp[I t]]], {t, t1, t2}], {r, r1, r2, 
    dr}],
  Table[ParametricPlot[ReIm[F[r Exp[I t]]], {r, r1, r2}], {t, t1, t2, 
    dt}],
  ParametricPlot[ReIm[(r Exp[I 4 dt])^2], {r, r1 + 5 dr, r1 + 6 dr}, 
   PlotStyle -> {Black, Thickness[0.01]}],

  ParametricPlot[ReIm[(r Exp[I 5 dt])^2], {r, r1 + 5 dr, r1 + 6 dr}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[ReIm[(r Exp[I 6 dt])^2], {r, r1 + 6 dr, r1 + 7 dr}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[ReIm[(r Exp[I 3 dt])^2], {r, r1 + 6 dr, r1 + 7 dr}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[
   ReIm[((r1 + 7 dr) Exp[I t])^2], {t, t1 + 3 dt, t1 + 6 dt}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[

   ReIm[((r1 + 6 dr) Exp[I t])^2], {t, t1 + 3 dt, t1 + 4 dt}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[
   ReIm[((r1 + 6 dr) Exp[I t])^2], {t, t1 + 5 dt, t1 + 6 dt}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ParametricPlot[
   ReIm[((r1 + 5 dr) Exp[I t])^2], {t, t1 + 4 dt, t1 + 5 dt}, 
   PlotStyle -> {Black, Thickness[0.01]}],
  ImageSize -> 200,
  Axes -> None,

  PlotRange -> All]

enter image description here enter image description here


I'm wondering if there is a way to make it significantly shorter since there are lots of repeating functions used.




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