story identification - Alien creature ends up taking over its whole planet. Starts small and takes over slowly

I've been trying to remember the title of this short SF story for ages now.

There is a creature (I think its actually immobile) that has a small plot of land on a planet. It starts growing and there is something to do with a small pool of water that it uses to help it breed/grow. It ends up taking over more and more of the planet's surface.

It's likely to be by a science fiction big name from the golden age (I think that's most likely anyway)

Answer

This sounds like it could be, not a short story, but rather a section of Peter F. Hamilton's "Commonwealth Saga" (Pandora's Star and Judas Unchained), specifically, there is a chapter in Pandora's Star where we learn the history of MorningLightMountain, an alien creature that is an immobile being served by mobile drone slaves, and extremely xenophobic.

Although not named, it could be characterized by its location: MorningLightMountain, a large cone of rock and earth that sprouted at the center of a long valley defined by rugged cliffs rising hundreds of meters from its swampy floor. Such was the alignment of the high walls that the thick beams of sunlight that the irregular edges produced swept across the central peak only during the morning.

A pool of water being relevant:

Two-thirds of the way up, they found a large pool fed by several of the gurgling streams. The four large motiles fused their thoughts together again and examined the area with their extended intellect. One of them sucked up some of the water, and found it contained a satisfactory level of Prime base cells swarming inside. Their presence confirmed the site would be suitable for an immotile, subject to a few alterations. A host of new instructions were issued to their fellow herd members.

and later:

Triggered by the nourishment contained within its food, MorningLightMountain’s reproductive organs began to ovulate. The first batch of a hundred nucleiplasms was discharged from its body into the water, allowing them to drift down to the large pool. Base cells began to congregate around them.

It begins to spread over the planet:

On the edge of the tropics, Prime immotiles were pushing farther and farther into the temperate lands, armed with their new knowledge and understanding of nature. Fire made it possible for them to live farther and farther from their original climate. Heated buildings, cultivated fields, canals, bridges, saws, and axes helped them travel farther and farther to establish allied territories.