The textbook figure you have here is for a transverse electromagnetic mode (TEM), which only has variations in two directions ($\hat y$ and $\hat z$), and moves in a third ($\hat x)$. These TEM-modes have particularly simple solutions. In more realistic cases, such as with moving charges and antenna's, the fields generated are far more complicated. The textbook figure is then educational, illustrating the main features of a simple case, while realistic cases have solutions more like the animation you added.
