Common does not mean trivial
The objects that appear most often in random Life soups are usually small still lifes and short-period oscillators. They deserve clear pages because users see them repeatedly before they know their names.
A block, tub, boat, beehive, and loaf all teach the same discipline from different shapes: inspect every live cell for survival, then inspect nearby dead cells for births.
Ash is a vocabulary
When a chaotic pattern settles, it usually leaves a field of ash. Naming the common ash objects lets a user describe what happened instead of only saying that the pattern stopped.
This is why the pattern library now gives several small still lifes their own pages. They are not only beginner examples; they are the objects users will keep seeing after longer experiments.
Oscillators add time to the catalogue
The blinker, beacon, toad, pulsar, and pentadecathlon show that a bounded object can keep changing forever. Their periods also make the idea of phase visible without needing a large board.
Together they form a practical reference set: period 2, period 3, common ash objects, and the named patterns users need to recognize in larger experiments.
Working takeaway
Treat common objects as the site vocabulary layer: short pages, runnable previews, and links back to the patterns that produce them as ash.