I would like to know, which implementation of random forest in package randomForest in R is used to grow decision trees? Is it CART, ID3, C4.5 ,...... or sth else?
According to ?randomForest() the description states:
randomForest implements Breiman’s random forest algorithm (based on Breiman and Cutler’s original Fortran code) for classification and regression. It can also be used in unsupervised mode for assessing proximities among data points, with Breiman L (2001). "Random Forests"." Based on: Machine Learning. 45 (1): 5–32. doi:10.1023/A:1010933404324.
According to Wikipedia (https://en.wikipedia.org/wiki/Random_forest):
The introduction of random forests proper was first made in a paper by Leo Breiman This paper describes a method of building a forest of uncorrelated trees using a CART like procedure. Reference to Breiman L (2001). "Random Forests". Machine Learning. 45 (1): 5–32. doi:10.1023/A:1010933404324. "
Therefore I would say it is CART.