Clear["`*"];  v = 1; t = 18; dt = 0.005; n = t/dt;  T = {{{0, 10}}, {{10, 10}}, {{10, 0}}, {{0, 0}}};  For[j = 1, j <= n, j++,   For[i = 1, i <= 4, i++,    x1 = T[[i, j, 1]];    y1 = T[[i, j, 2]];    If[i != 4,     x2 = T[[i + 1, j, 1]];     y2 = T[[i + 1, j, 2]],      x2 = T[[1, j, 1]];     y2 = T[[1, j, 2]]     ];    x1 = x1 + (v dt (x2 - x1))/Sqrt[(x2 - x1)^2 + (y2 - y1)^2];     y1 = y1 + (v dt (y2 - y1))/Sqrt[(x2 - x1)^2 + (y2 - y1)^2];     T[[i]] = Append[T[[i]], {x1, y1}]    ]   ];  Graphics[{Line[T], Line[{{0, 10}, {10, 10}, {10, 0}, {0, 0}, {0, 10}}]}] 

This code for solving MiceProblem in the procedural style, is it possible implement by functional style? Table or Nest may required. I only can replace For with Do.