Problem:

I have been thinking a little about the origins of life, and was further inspired by this question: How did the first self replicating organism come into existence?
I can accept that we don't quite know exactly how, but has any large-scale/long-term simulation been carried out?
There have been experiments but they seem to have been on a small scale. As an example, according to the Abiogenesis page on Wikipedia, some experiment which spontaneously formed peptide structures was carried out by Sidney Fox during the 50s and 60s.

What would be really interesting is if there had been some experiments or simulations carried out during a very long time, plausibly allowing for extremely low-probability structures to form. I doesn't matter whether this simulation/experiment has been carried out in a lab or as a computer simulation. There is of course the interesting but old "Conway's Game of Life" simulation, but according to my search efforts nobody has really tested it on a very large scale and in 3D.

Again, I'm looking for something extensive, like a decades-long single lab experiment or a simulation that has been run for years. Please express in detail.