There is only one charged particle at the origin which is accelerated as sine-wave.
The oscillating charged particle will produce changing electric field, which in term induced magnetic field at the next instance.
The induced oscillating magnetic field re-generate electric field at the near space.
The above process continue and produce the electromagnetic field.

The EM wave move with constant speed in the x-direction in the above simulation. I am sorry that It give you wrong impression and make you confused. Sorry!