Cell Division Puzzle

On YouTube, I recently watched this puzzle introduced by creator @3blue1brown. I figured it would be a pretty easy puzzle and probably involved factorials or exponentials if you wanted an exact numerical answer. I didn't think of it much until a few weeks later when he posted the solution. But before you watch it, read this! I promise, it will be quick.

By now you probably have seen the puzzle video, but if you haven't, go ahead and watch it. I'll get straight to the point. I figured it could be solved rather quickly. After all, you only have to free up a 3x3 grid. Each time a cell divides, it frees up one tile. So that would mean that there would be at least 9 steps to solution, likely more, but at least 9 gives us a starting estimate. Graphically speaking, in my mind at least, you could free up rows one-by-one by dividing cells sequentially which would just "push" your row down by one.

When I saw the solution, I thought there was absolutely no way that his answer was correct; but his math made perfect sense. And numbers don't lie. I couldn't accept it, so I coded up this game called Cellsplit to graphically work out this exact puzzle. Why don't you try it out before watching the solution? It will blow your mind. If you like math.