Modelowanie2

r = 0.1;
x0 = 0;
y0 = 0;
z0 = powierzchnia[x0, y0];
listaKatow = Table[RandomReal[{0, 2 Pi}], {i, 500}];
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 = {};

While[i <= 500, alfa = listaKatow[[i]];
 Result =
  FindInstance[{(y - y0)*Cos[alfa] - (x - x0)*Sin[alfa] == 0,
    f[x, y, x0, y0, z0] == 0}, {x, y}, Reals, 2];
 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++;]


rows = List[];
n = 1;
While[n <= 500,
 r0 = points[[n, 1]]^2 + points[[n, 2]]^2 + points[[n, 3]]^2;
 rows = Append[rows, {r0, n, r0/n}];
 n = n + 1]

srednia = Mean[rows[[All, 3]]];
odchylenie = StandardDeviation[rows[[All, 3]]];

Print["Średnia:", srednia];
Print["Odchylenie standardowe:", odchylenie];

rows = Insert[rows, {"r^2", "t", "r^2/t"}, 1];
Grid[rows[[;; ;; 10]], Frame -> All]


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, 500, 1}]