TrueRevan: Hi,
I just found one of those huge asteroids and while finding those with antimatter or with face of gozu is hard but possible, I was amazed when I bumped into huge CRYSTAL asteroid which drops progenitor shard... I don't know maybe for others it is nothing special but I didn't know those even existed. Some random mission brought me there, otherwise I would never find it. It is located in empty space, not in some nebula and I wasn't able to find any clue how to find other asteroids like that. Please tell me your experience with this one. I took some screenshots if you want to see it. BTW sorry for my bad english. :/
AFAIK, there is a Gozu-rich cluster, and an obsidian-AM cluster in EVERY system. They are, of course, tiny, difficult to distinguish on any but the closest map settings, and they are never named or marked even after you have visited them. Keep good notes of where you find them in any system.
In years of playing I have never been able to decide if the PS crystal asteroids occur in every system, though the evidence of the other two types would tend to suggest that. I HAVE certainly found them in systems beyond the first one.
The trick to doing a usually reliable grab on the PS, is to fly your ship right up in contact with the crystal asteroid. Then blast like crazy while hovering one finger over the E key, or whatever the pad equivalent is. Watch the damage meter for the asteroid and the instant it is exploding, jam the the E key and hold it. Your ship should be closest, and you should get a good grab before the other circling mining ships react. As soon as you hear the hiss of the tractor stop, jab it again, just in case.
The Gozu cluster and the anti-matter cluster in each system are apparently always found somewhere in the rightmost 25% of the system map ... somewhere. Beyound that hint you just have to search.
BTW, IMHO the common description of the distant appearance of the Gozu cluster as "blue", "light blue", "blue-green", or "greenish" is inaccurate and misleading. The nebula is the same misty white as all the other white nebulae. but it is small, not very big/deep, and not dense. It is also filled with a great mass of sorta black, bluish, or occasionally greenish metallic asteroids. At times on approach this may make the cloud look a little tinted, but in my experience it more often looks like wispy cotton with some black seeds left in. Of course, other white nebula + tetrahedrite field belts can also look like this from a distance, but after you get some experience with these you will sense that in the "magic" clusters, the specks are a little more pronounced. (They are, after all, huge.) The other clue once the cloud is in distant sight is that this nebula / belt is tiny compared to most other white clouds.
As far as spotting it on the map, good luck. It is possible, but only on the 2-3 closest magnifications, and searching that way is quite tedious. And on the map, this clound is TINY. And often disappears into the less defined edges/boundaries of other nearby nebulae. I usually find them a) by accident, combined with being alert for it when I am working in the "Eastern" quarter of the system, or b) by methodically mining, or at least searching, EVERY belt and nebulae from the right edge of the system inwards.