I am not sure a fractal have to start from the bottom and increase in subdivisions.
For example, I believe the Mandelbrot set is all there at the same instant, but, because we can not calculate to infinity we have to limit the iterations.So in this case I don't think there is beginning or end to this fractal, or even the notion of subdivisions.
If you look how the DNA become a chromosome you can see it start in parts and become a whole.
I can increase the iterations by increasing the number of initial circles.
In the video, you can see that it is very easy to add as much circle I want. They place themselves side by side.
I could also make a simple equation to place equally those circles at equal distances.
What I like in this ''fractal'' is that the notion of chaos is the base of it existence.
Without chaos or incertitude, all the circles would converge to the centre in a straight line.
But because we can not determine with a infinite precision the position of the object, one circle will be more attracted to the left or right, and follow a chain reaction!