CC[m_, t_] := Module[{n, M, a},

  n = Dimensions[m][[1]] - 1;
  M = Table[0, {i, 0, n}, {j, 0, n - i}];
  a = Table[" ", {i, 0, n + 1}];
  M[[1]] = m;
  a[[1]] = ListPlot[m, Joined -> True, DisplayFunction -> Identity];

  For[i = 1, i <= n, i++,
   For[j = 1, j <= n - i + 1, j++,
    M[[i + 1, j]] = t*M[[i, j + 1]] + (1 - t)*M[[i, j]]];
      a[[i + 1]] =
    ListPlot[M[[i + 1]], Joined -> True,
     PlotStyle -> RGBColor[i/n, 0, 1 - i/n],
     DisplayFunction -> Identity]];
  a[[n + 1]] =
   ListPlot[M[[n + 1]], PlotStyle -> PointSize[0.05],
    DisplayFunction -> Identity];
  a[[n + 2]] =
   ParametricPlot[
    Sum[Binomial[n, k]*s^k*(1 - s)^(n - k)*m[[k + 1]], {k, 0, n}], {s,
      0, t}, PlotStyle -> {RGBColor[1, 0, 0], Thickness[0.02]},
    DisplayFunction -> Identity];
  Show[a, DisplayFunction -> $DisplayFunction,
   AspectRatio -> Automatic, PlotRange -> All, Axes -> False]]
(test)
m = {{0, 0}, {0, 1}, {1, 1}, {2, 0}, {3, 1}};
Animate[CC[m, t], {t, 0.01, 1}]