# Why isn't the vector field being plotted over the entire torus?

I am trying to plot a vector field over a torus. Here is my code and the image it produces:

f[x_, y_, z_] = x^2 + y^2 + z^2;
x[u_, v_] = 4 + (3 + Cos[v]) Sin[u];
y[u_, v_] = 4 + (3 + Cos[v]) Cos[u];
z[u_, v_] = 4 + Sin[v];

ParametricPlot3D[{4 + (3 + Cos[v]) Sin[u], 4 + (3 + Cos[v]) Cos[u],
4 + Sin[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi},
PlotStyle ->
Texture[
StreamPlot[
Evaluate[D[f[x[u, v], y[u, v], z[u, v]], {{u, v}}]], {u, 0,
2 Pi}, {v, 0, 2 Pi}, Frame -> None, ImageSize -> Large]],
Mesh -> None, ImageSize -> Large, PlotPoints -> 100,
PlotRange -> {{0, 8}, {0, 8}, {0, 7}}] The vector field isn't plotted around the outside of the torus, how do I get Mathematica to plot the entire vector field?

PlotRangePadding -> None.

StreamPlot[
Evaluate[D[f[x[u, v], y[u, v], z[u, v]], {{u, v}}]], {u, 0,
2 Pi}, {v, 0, 2 Pi}, ImageSize -> Large, PlotRangePadding -> None] ParametricPlot3D[{4 + (3 + Cos[v]) Sin[u], 4 + (3 + Cos[v]) Cos[u],
4 + Sin[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi},
PlotStyle ->
Texture[StreamPlot[
Evaluate[D[f[x[u, v], y[u, v], z[u, v]], {{u, v}}]], {u, 0,
2 Pi}, {v, 0, 2 Pi}, Frame -> None, ImageSize -> Large,
PlotRangePadding -> None]], Mesh -> None, ImageSize -> Large,
PlotPoints -> 100, PlotRange -> {{0, 8}, {0, 8}, {0, 7}}] 