Can builders stack conversation chips into piles faster than the chips decay? Amber patches hold chips (orange would be a pile); the amber thins out tick by tick.
Try this Choose Cathedral threads (branching 55, decay-rate 5), then lower decay-rate to 2 while it runs (it takes effect live). chip-patches still falls, only more slowly, and no pile forms.
About this model Where it ends up The run stops after 200 ticks. In every preset the board ends nearly empty: chip-patches near 0, pile-patches 0, and your-drops-count around 20.
A MathPets model of conversation threads as termite construction, after the classic termite chip-piling model, seeded from aggregate X statistics (no post text is used). Chips stand for conversation: builders pick them up and drop them elsewhere, you add new ones when you post, and chips decay at random. A pile is a patch holding 3 or more chips. The run lasts 200 ticks.
Setup puts one chip on chip-density percent of patches. Each tick, every patch with chips loses one with probability decay-rate percent. You wander, post with a chance that peaks at peak-hour (adding a chip to your patch), and sometimes carry a chip and drop it, possibly onto another chip. A builder picks up a chip it walks onto with probability 40 + reply-share/3 percent, carries it, and drops it on an empty patch; branching and quote-share set how soon.
Builders only ever drop onto empty patches, so only your own drops can stack chips, and decay removes chips faster than you add them. In every preset the board empties within about 100 ticks and pile-patches stays at 0; even at the slowest decay (2%), no pile forms in 200 ticks.