A computer algorthym might show a model of how evolution might happen, but there is more that has to happen. You need examples in the real world. Evolution has this. You have to have real world data. The algortithm only gives some kind of explaination for the data that is observed. The algorithm in and of itself is not enough. It has to be able to mimic the actual data.
You are also drawing upon the vast amounts of evidence from the real world for your conviction though.
The algorithm in and of itself shouldn't convince you. It is the algorithm that fits into what we observe in the real world that makes it a strong statement.