Animacja

r = 0.1;
x0 = 0;
y0 = 0;
z0 = powierzchnia[x0, y0];
listaKatow = Table[RandomReal[{0, 2 Pi}], {i, 100}];
powierzchnia[x_, y_] = 2 x + 3 y^2;
f[x_, y_, xp_, yp_,
   zp_] = (x - xp)^2 + (y - yp)^2 + (2 x + 3 y^2 - zp)^2 - r^2;

i = 1;
points = {};

SeedRandom[1234];

While[i <= 100, alfa = listaKatow[[i]];
 Result =
  Solve[{x, y} \[Element]
     InfiniteLine[{{x0, y0}, {x0 + Cos[alfa], y0 + Sin[alfa]}}] &&
    f[x, y, x0, y0, z0] == 0, {x, y}];

 xPunktu = Result[[1, 1, 2]];
 yPunktu = Result[[1, 2, 2]];
 zPunktu = powierzchnia[xPunktu, yPunktu];
 pointCurrent = {xPunktu, yPunktu, zPunktu};

 xPunktu2 = Result[[2, 1, 2]];
 yPunktu2 = Result[[2, 2, 2]];
 zPunktu2 = powierzchnia[xPunktu2, yPunktu2];

 pointCurrent =
  RandomChoice[{{xPunktu, yPunktu, zPunktu}, {xPunktu2, yPunktu2,
     zPunktu2}}];

 points = Append[points, pointCurrent];
 x0 = pointCurrent[[1]];
 y0 = pointCurrent[[2]];
 z0 = pointCurrent[[3]];

 i++;]

Animate[Show[
  Plot3D[{2 x + 3 y^2}, {x, -1, 1}, {y, -1, 1},
   BoxRatios -> {1, 1, 1}],
  Graphics3D[{Green, PointSize[.02], Line[points[[;; it]]],
    Point[points[[it]]]}]], {it, 1, 100, 1}]