From Bard. Any hits?

Based on your description, there are a few possibilities for the movie title:

Annihilation (2018): This sci-fi horror film features a mysterious, shapeshifting entity from another dimension that resembles a shimmering mass of cells. It has a singular yellow eye and its goal is to consume and assimilate everything in its path. While not explicitly biological computers, the film explores themes of consciousness and adaptation within biological systems.

The Thing (1982): This John Carpenter classic depicts a shapeshifting alien parasite that can imitate any living organism. Although not from another dimension, it exhibits the amorphousness and tentacle-like appendages you mentioned. Additionally, a large eye is shown briefly when the creature transforms into a dog.

Videodrome (1983): David Cronenberg’s body horror film delves into the intersection of technology and flesh. While not featuring a transdimensional monster, it has grotesque imagery of bio-technological merging and mutations, which might share some thematic similarities with your description.

However, based on the detail about “biological computers” specifically, there’s a chance it could be a smaller indie film or one outside the mainstream.