I am creating a device similar to the one on the link above except I will be using a PIC chip to control the transistors to create special patterns.
One problem I've run across is that if I activated the top transistor on the side and all of ones along the bottom (to turn on the LEDs on the whole top row) how would I then turn on just one LED on the second row? Surely activating the second transistor down will allow the entire row to light because of all the bottom transistors being active?
I'm guessing that either I've gone wrong somewhere (fairly likely ) or that I'm going to need some kind of multiplexing system.
Yes, that is exactly what you need to do. That way only one row and one column is on at a time. You switch them really fast so several LEDs appear to be on at the same time.
The circuit lights one LED at a time in sequence because only one output of each CD4017 is high at a time.
If you speed up the oscillator then all the LEDs will appear to be lighted at the same time but they will look dim.