Where is the array problem in the first variable of ListPlot3D in Mathematica?

Question

i want to draw the evolution of a function in the time with ListPlot3D, the code is:

Clear[f0, fval, x, f]
f0[x_] = E^(-4 (x - 1)^2);
x[t_, x0_] = x0 + f0[x0] t;
f[t_, x0_] = f0[x0];
fval[t_] := Table[{x[t, x0], f[t, x0]}, {x0, -5, 3, 0.1}]
ListPlot3D[{Table[
Table[{x[t, x0], t, f[t, x0]}, {x0, -.5, 3, 1}], {t, 0, 2, 0.1}]}]

But mathematica give me the error "must be a valid array or a list of valid arrays"

Answer 1

Your nested Table have extra layers of {} around parts of it.

Change it to

ListPlot3D[Partition[Flatten[{Table[
  Table[{x[t, x0], t, f[t, x0]}, {x0, -.5, 3, 1}], {t, 0, 2, 0.1}]}],3]]

which gets rid of ALL the extra {} and then only puts back enough to wrap each triple in {}

There must be some reason why ListPlot3D doesn't understand nested rows of triples.