A:Answer Short answer is yes. The colors automatically change on a continual clock wise cycle. The fans are all in sync, including the one in the back of the PC.
To change them, you will need to download the appropriate utility based on the motherboard. e.g. Polychrome RGB for ASRock or Dragon Center for MSI. Depending on the features of the utility, the fan colors can pulse, flash rotate or be steady at any color. Some utilities have the option of having the colors change based on your gaming actions or temp of your CPU.