Undecidability conjecture for amoeba-colony growth

Let $\ell$ be an integer, let $T$ be a tree, and let an amoeba colony be a finite set of ordinary amoebas $\mathcal{C}=\{A_1,\dots,A_n\}$. A growth sequence for $\mathcal{C}$ is obtained by repeatedly choosing an alive amoeba in the colony and performing an $\ell$-growth from the current tree.

Amoeba-colony undecidability conjecture. The following algorithmic problem is undecidable:

• Input: an integer $\ell$, a tree $T$, and an amoeba colony $\mathcal{C}$.
• Question: is there an infinite growth sequence for $\mathcal{C}$ starting from $T$?

The proposed undecidability would follow from the conjectured ability of amoeba colonies to simulate universal computation. The source presents this as a direction for future work, and no resolution is supplied.