you should look into shift registers with PWM functionality. it might be tedious wiring though. maybe a dmx driven led panel can get you much further, if you are working with grid of LEDs anyway (according to your sketch).
teensy3.0octows2811-led-control
I’ve done exactly this with a teensy board, which is an ARM powered clone of arduino, you can control upto 1000 odd LED’s from 1 board, although if its for your thesis, that might be cheating!