Characteristics of growing, tangled branches

Multicellular organisms often exhibit morphologies featuring branching chains of cells. Examples include root systems, mycelial networks, cyanobacterial mats, and dense brush and bushes. Notably, filamentous, branching objects can wind around each other, thus forming tangles that are difficult to disassemble. This phenomenon, called "entanglement'', is well-known to occur in non-growing materials. However, entanglement is typically studied in non-living, and thus non-growing materials, such as polymers. Further, with few exceptions, currently studied systems are filamentous rather than branching, and generally flexible rather than rigid. Much less studied is the emergence of entanglement in the regime of growing, branching, and relatively rigid systems, despite their prevalence across the domains of life. Consequently, many open questions regarding entanglement remain unclear: how readily does entanglement emerge in growing systems? Do predictions for static components remain relevant for these non-equilibrium cases? Here, we use a combination of experiments and simulations to show that entanglement through growth is easy to achieve, can result in configurations that are impossible to access through mechanical agitation alone, and can be tuned through branch geometric changes.