## Showing Exponential Growth in Bacteria

So I got an interesting request from the math department at Sapling Learning about a week ago. We wanted to show the concept of exponential growth, using bacteria as the example. So one bacterium divides into two and they each divide into two and so on. We decided to take this through six generations landing us with 64 bacteria on screen by the end of it.

So the catch was, how to move 64 bacteria around as one, and then as two with an equal number of divisions nested inside and then as 4, each with an equal number of divisions inside, and then as 8 and so on. So I got a little complicated with my object hierarchy for this one.

So I had one called cp_start, short for clostridium perfringens (a bacterium capable of reproducing at the 15 minute generation cycle that we wanted for the example) with a bend object on it. And then nested within that one was a duplicate called cp_15, another called cp_30, cp_45, cp_60, cp_115, and cp130, to represent the ones that would branch divide off at the 15 minute, 30 minute, 45 minute, hour, hour 15, and hour thirty points from that one, all with their own bend objects. Then within each of those I had further duplicates that would still occur from each of those. Within cp_45 there was cp_60, cp_115, and cp_130, but cp_60 would only have cp_115 and cp_130. And then so on with each bacterium.

In the end it worked out, and the extra arranging effort was well worth it as the sprawl pattern of bacteria had to be adjusted after the first time. My first attempt had them all more compactly arranged, but one of our biology experts explained that bacteria could only continue a regular exponential growth cycle if they were able to get to more food. If I hadn’t had them nested like this, it would have been incredibly hard to go back and make them disperse further.

I added the timer and count in After Effects. The whole thing plays at a sped up pace, showing one minute per second of animation. And I think it looks good. I hope that we get to use it for biology content someday as well as for the math example now.