You can store whatever in processing. You are the programmer. Make a game plan.
So you have to explain the data coming in to us as well. So this is a heart monitor. Why is it so erratic. Is each vertical pixel line represent an electrical pulse and time interval? why is the serial coming in as groups of 5? If you post the arduino code and how the sensor works, it would help a lot.
Wish you luck 'cause I don't know. You might have better luck in the processing forum as this is a visualization issue more than anything.
I have a feeling the way you're rendering the electrical pulses is wrong. If you want to make to look like the heart beat chart, you'll need to make the pixel 'MOVE/animate' to the point of peak, not draw directly to the peak.