Clear["Global`*"]

\(\(\( (*to\ avoid\ annoying\ messages*) \)\(
\)\(\(Off[
        General::spell];\)

    \(Off[General::spell1];\)\)\)\)

(* histogram maker,  
      far from perfect! Do not use for generic purposes*) 
histo[list_, nubin_] := 
      Module[{newlist, mi, ma, inbin, dim, tab, xx, 
          yy}, 
Do[
          inbin[ll] = 0, {ll, 1, nubin + 1}]; 
newlist = 
          list; 
epsi = (Max[newlist] - Min[newlist])/
            10000; 
mi = Min[newlist] - epsi; 
        ma = Max[newlist] + 
            epsi; 
dim = Dimensions[
              newlist][[1]]; 
Do[
          ww = Floor[((newlist[[ll]] - mi)/(ma - mi))*
                  nubin] + 1; 
inbin[
              ww]++
, {ll, 1, 
            dim}]; 
 (* 
          I put the boundary of the last bin in the last bin*) 
inbin[nubin] = 
          inbin[nubin] + inbin[nubin + 1]; 
Do[
          xx[2*ll] = 
            mi + (ll)*(ma - mi)/nubin; 
xx[
              2*ll + 1] = 
            mi + (ll + 1)*(ma - mi)/nubin; 
yy[
              2*ll] = inbin[ll + 1]; 
          yy[2*ll + 1] = inbin[ll + 1], {ll, 0, nubin - 1}]; xx[-1] = mi; 
        yy[-1] = 0; xx[2*nubin] = ma; 
        yy[2*nubin] = 0; 
tab = 
          Table[{xx[ll], yy[ll]}, {ll, -1, 
              2*nubin}]; 
Return[
          ListPlot[tab, PlotJoined -> True, 
            PlotRange -> All]]]

f[x_] := 1 - a*x^2; a = 2;
t1 = NestList[f, 0.3, 10000]; histo[t1, 100]