Running Blender python script outside of blender

I want to visualize some scientific data, which is, at the moment, only an animation of some spheres with different colours and sizes.

I already created a script within Mathematica which creates the input for POV-Ray.

My problem is, that I'm not satisfied with the quality of POV-Ray's results and wanted to write a Python script, which could set up the corresponding blender scenes and render them. An important constraint is, that I want to render on a headless machine, so I can't use Blender's internal console.

My question: Is it possible to use Blender's api from an external console to get POV-Ray-like behaviour?

After reading George Profenza's answer I did further research and found Don’t Use Blender! in Blender's documentation.

In contrast to my thoughts, one has to create a python script which is executed by blender in background mode.

./blender --background --python myscript.py

#blender