I make kombucha* at home and observe something similar whenever I start a new batch using a small piece of culture taken from an old container. Either the yeast or the bacteria - or both in symbiosis - form the typical stringy structures seen in so many petri dishes, that radiate from the "mother" outwards to the edges of the container. As time passes, each area isolated between the crossing strings slowly thickens on the surface and eventually merge with the rest of the growth as a single colony.
* https://en.wikipedia.org/wiki/Kombucha