Is it possible to achieve a similar result with Blender?
What follows is a sloppy facsimile to demonstrate technique not artistry. You are the artist. The background use is black for legibility. I have no idea of your future background. Blender Render not Cycles. No lights. Emission material.
over a photo with Gimp
Your writing seems to imply you want a transparent background.
Any single or range of frames can be rendered and saved to disk with a transparent background.
Because you state you only want one image and not a sequence that can be critiqued as a moving image you might just need a circle or sphere mesh and generate particles or spherical texture for density. Forces are convenient. The movement or location might come from the [normal velocity] of the Blender Particles System. Color and Blur if that suits you in the Compositor
The particles themselves can be group of mesh objects or PNG bill board images. You can also generate all particles in 1 or 2 frames and by the 3 frame the image is static if there are not forces, normal velocity, gravity or similar. Splurge and generate a few hundred images and pick the one you want. Since the shape is generally circular spherical you can layer PNGS with rotation for increased density.
If you do not value your originality, and the mentioned image is intended for sharing you could you can also remove the background from the image. GIMP or Blender Compositor.