Does Voilence lead to...more voilence?

From reading this playwrite, if there was one thing i learnt, it was that, voilence, definatly does lead to more voilence. Act 3 is when it all started. Ceaser assasination started a short, but brutal chain of voilence in Rome. You see, after Anthony managed to get the croud on his side to go against the conspirators, that croud grew into an angry, bloodthirsty mob. On a few occasions they were all yelling "Burn! Kill! Rip them to pieces!...etc" when trying to find the conspirators. In their craze, they even killed a random person only because he had the same name as one of the conspirators (Cinna the Poet). Then, as we watched in the movie about Acts 4 and 5, there was a massive battle between the forces of Brutus and Octavius's Army, which means hundreds of people dying. Then there was after the battle, when Cassius and Brutus, both suicide, seeing that there lives were pretty much destroyed now. Rome lost a few very important figueres in this timespan, and also many innoccents. Who knows, there might have been more killings in this time, but it just wasnt mentioned.