Aha! 

Here is the wireframe, which tells you virtually nothing, so I've added some extra screenshots to explain what's going on.  The apparently multiple spheres are really one sphere - if you look carefully in the posted picture, you can see a couple of artefacts that give the game away.  It makes use of Bryce's amazing ability to render volumetric materials in full 3D glory.  I began with a standard Bryce procedural 3D volumetric texture;  this originally made use of the alpha you can see in Texture A channel in the Material Editor, and would have rendered the sphere look like it does in the small inset picture.  I then loaded another alpha to replace this one, again a standard Bryce one, called "Blue Dots" into the Texture B channel, and set Texture B as the source for the Base Density.  This then produces a set of spheres in effect carved out of the original sphere, if you will, as in the posted render.  However, where the volumetric shapres intersect the surface of the sphere, they get cut off.  On the right, I have set the diffuse channel to bright green and also changed the value of the base density as well as the scale of the "Blue Dots" alpha - this is still the same single sphere, but now it's almost full of solid volumetric texture, which hopefully illustrates the effect better.  It's really only the same principle behind the "Ball Bearings" 3D volumetric preset that ships with Bryce, or indeed any volumetric texture.  Amazing stuff!

 

 

My self-build system - Vista 64 on a Kingston 240GB SSD, Asus P5Q Pro MB, Quad 6600 CPU, 8 Gb Geil Black Dragon Ram, CoolerMaster HAF932 full tower chassis, EVGA Geforce GTX 750Ti Superclocked 2 Gb, Coolermaster V8 CPU aircooler, Enermax 600W Modular PSU, 240Gb SSD, 2Tb HDD storage, 28" LCD monitor, and more red LEDs than a grown man really needs.....I built it in 2008 and can't afford a new one, yet.....!

My Software - Poser Pro 2012, Photoshop, Bryce 6 and Borderlands......"Catch a  r--i---d-----e-----!"