Benford's Law Visualisation

(*this code is terrible, sorry!*)
frame[t_] :=
 Module[{markers, \[Alpha], random, firstdig, list, frame, \[Delta],
   fn, bc, xlabs, data},
  markers = Flatten[Table[i 10^n, {n, 0, 3}, {i, 9}]];
  firstdig[i_] := Module[{x = Mod[i, 9]}, If[x == 0, 9, x]];
  \[Alpha] = 0.8;
  random := Times @@ RandomReal[{\[Alpha], 1/\[Alpha]}, t];
  list = Table[random, {i, 500}];
  bc = BinCounts[Log /@ list, 1];
  bc = 2 bc/Max[bc];
  xlabs = Range[Log@Min[list], Log@Max[list], 1];
  data = Partition[Riffle[xlabs, bc], 2];
  (*data=Select[data,0<#[[1]]<Log[Max[markers]]&];*)
  fn = Interpolation[data];
  \[Delta] = 0.09;
  frame = Show[
    Graphics[{
      Table[{
        Text[
         firstdig[
          i], {(Log[markers[[i]]] + Log[markers[[i + 1]]])/2, -1.2}],
        ColorData["Rainbow"][Mod[i, 9]/10],
        Rectangle[{Log[markers[[i]]], -1}, {Log[markers[[i + 1]]], 0}]
        }, {i, Length@markers - 1}],
      {
       Text[Style["units", Medium], {0.5 Log[10], -1.6}],
       Text[Style["tens", Medium], {1.5 Log[10], -1.6}],
       Text[Style["hundreds", Medium], {2.5 Log[10], -1.6}],
       Text[Style["thousands", Medium], {3.5 Log[10], -1.6}]
       }
      }, ImageSize -> {320, 180}]
    ,

    Graphics[{EdgeForm[],
      Table[
       {ColorData["Rainbow"][First@RealDigits[Exp[ x + 0.05]][[1]]/10],
        Polygon[{{x, 0}, {x + \[Delta], 0}, {x + \[Delta],
           fn[x + \[Delta]]}, {x, fn[x]}}]}
        , {x, Max[0, Min[First /@ data]],
        Min[Max[Log /@ markers],
          Max[First /@ data]] - \[Delta], \[Delta]}]
      }]
    ];
  frame
  ];

frame[100]