Venus flytraps count electrical impulses to induce the digestive process (2016)

Mimosa pudica is another fast-moving plant, which isn't carnivorous (and not closely related)

Some Drosera (sundew) species actively curl their leaves around prey, but rely on the prey being stuck to their leaves already, so different to the mechanism of a VFT. Drosera and VFT are in the same family, so are pretty closely related.

There's Utricularia (bladderworts) which are capable of catching prey rapidly, but the plant itself doesn't really move I guess.

> Where are the other fast moving plants?

Seems there is a bunch of them: https://en.wikipedia.org/wiki/Rapid_plant_movement

I believe most carnivorous plants evolved while living in areas with depleted soil resources. Presumably, during that time, there was some sort of selection for plant mutants that were slightly more likely to survive because they could absorb nutrients from decaying insects, but without any sort of physical trap mechanism. Then, over time, some small physical mutations showed up (and provided a survival and reproduction benefit)... and ... well, to be honest, speculating about evolution like this is remarkably iffy. But we can speculate they probably happened through modifications of existing plant primitives, like leaf structures.

Dawkins made an attempt at it in The Blind Watchmaker. See also https://www.smithsonianmag.com/science-nature/how-carnivorou... and https://www.nature.com/articles/nature.2017.21425