Ruler Scaling

n = 10;
corners = {{0, 0, 0}, {0, 10, 10}, {1, 0, 0}, {1, 10, 1}};
f = Interpolation[corners, InterpolationOrder -> 1];
frame[t_] := Quiet@Graphics[{
     ColorData["DarkRainbow"][1],
     Line[{{0, 0}, {0, 1}}],
     Table[{ColorData["DarkRainbow"][0.3^(s + t)], Table[
        If[f[t, i/10^s] <= 1,
         Line[{{f[t, i/10^s], 0}, {f[t, i/10^s], 0.3^(s + t)}}], {}]
        , {i, (n + 1) 10^s}]}, {s, 0, 3}]
     }, PlotRange -> {{0, 1 + 0.01}, {0, 1}}, AspectRatio -> 1/3,
    ImageSize -> 300];
Manipulate[frame[t], {t, 0, 1}]