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2 Specified the perturbation in the light of Scott's incisive observation.

Imagine $n$ $z$-vertical sticks uniformly spaced around a unit-radius circle in the $xy$-plane. At $t{=}0$, each is randomly $\epsilon$-perturbed from the vertical, and they fall under the influence of gravity. Will some sticks form a "teepee" suspended above the $xy$-plane?

Let us assume the sticks are one-dimensional segments of height $h$, perhaps $h{=}2$ so they span the diameter, and that their base points are pinned to the plane via universal joints. It seems possible that a subset of sticks could fall to form a weaving with a cyclic on-top-of graph, as illustrated below.

Assuming a sufficient coefficient of friction $\mu$ between pairs of sticks, it seems conceivable that such a structure would not collapse to the plane.

What is your intuition here? For sufficiently large $n$, and adequate $h$ and $\mu$, would some sticks form a woven structure above the plane? Or would all sticks ultimately flatten to the plane? If the latter, are there natural conditions that would lead to formation of a "teepee"? I am less interested in probability calculations than in a qualitative assessment.

I've tagged this 'recreational' because it is only a peripheral spinoff of my research.

Addendum. It is now clear, from the comments of Scott Morrison and Rahul Narain, that the random perturbations should be random both in direction and magnitude. Otherwise, as Scott incisively observed, the sticks, with high probability, all fall without touching one another until they reach the plane (which to me is already rather remarkable!).

1

When sticks fall, will they weave?

Imagine $n$ $z$-vertical sticks uniformly spaced around a unit-radius circle in the $xy$-plane. At $t{=}0$, each is randomly $\epsilon$-perturbed from the vertical, and they fall under the influence of gravity. Will some sticks form a "teepee" suspended above the $xy$-plane?

Let us assume the sticks are one-dimensional segments of height $h$, perhaps $h{=}2$ so they span the diameter, and that their base points are pinned to the plane via universal joints. It seems possible that a subset of sticks could fall to form a weaving with a cyclic on-top-of graph, as illustrated below.

Assuming a sufficient coefficient of friction $\mu$ between pairs of sticks, it seems conceivable that such a structure would not collapse to the plane.

What is your intuition here? For sufficiently large $n$, and adequate $h$ and $\mu$, would some sticks form a woven structure above the plane? Or would all sticks ultimately flatten to the plane? If the latter, are there natural conditions that would lead to formation of a "teepee"? I am less interested in probability calculations than in a qualitative assessment.

I've tagged this 'recreational' because it is only a peripheral spinoff of my research.