2025-258

A fungal colony, whose hyphae form a network called the mycelium, started growing on a piece of bread left unattended. The colony started small, at an initial number of spores \(N = 5000\). It is known that, although the number of spores remains constant, this species creates hyphae (links) over time, so that at any point in time it looks like a random \(G(N,p)\) network, where \(p\) is given by the function below:

\( p(t) = t/10^{4}\)

where t is the time measured in days.

Given two different intervals:

• A day has passed
• Three days have passed\

Assign the correct alternatives with respect to attributes about the mycelium growth.

1. As one day passes, the network is subcritical, and by three days, it remains subcritical.
2. As one day passes, the network is subcritical, and by three days, it’s supercritical.
3. As one day passes, the network is critical, and by three days, it’s supercritical.
4. As one day passes, the network is already supercritical.
5. None of the above.

Original idea by: Alexandre Petrachini