>> OK so I quickly modified my existing RK4 code to do integration steps on 
>> 1728*972 particles in 2D with 4x 1/r attractors.  So it takes about 2.5 
>> seconds per integration step, does this compare with your results?
>
> It's roughly comparable, certainly.
>
> (What hardware are you running it on?)

That was using 1 core of an Intel E8500 @ 3.16 GHz.

Of course someone has already done particle system simulation on the GPU 
before:

http://2ld.de/gdc2004/

Running option 2 of that demo on my GPU gives 15fps for a million particles, 
so for 1728x972 I make that about 9fps.  If you restrict it to 2D rather 
than 3D it should go a little faster.

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