Multiple rgb control plus calculation help
It's not advised to connect leds in parallel, with only one common resistor. Slight difference in forward voltage of the leds will create big current differences. This will make some leds appear brighter that neighboring leds. It can also damage the brighter led since too much current can flow through them. So you need to add a resistor to each led, and common the other side of these resistors to the transistor. 

Second bigger error is that there isn't any resistor between the arduino pin and the base of the transistor. Without it there is nothing limiting the current going into the base, which could fry the arduino pin.