Richard Archer-Jones wrote:

It's a bit like the old 'butterfly's wings' theory whereby the effect
of such an activity by such a small creature could, by a myriad of
follow on causes and effects, eventually cause something big to happen.

I think you mean "the butterfly effect", so-called because in "The
Sound of Thunder", a 1952 short story by Ray Bradbury, a time traveler
to the dinosaur era steps off the path and steps on and kills a
butterfly, resulting in a significantly changed world when he returns.

- Herb