2. Does the fractal model also work for dynamic, fluid or changing shapes?
Yes, in fact this is it’s most ‘natural home’ I think. The reason is that fractals are about processes, not things, and processes are just that: descriptions of changes, not of things, and changes have a way of, well, being DIFFERENT the next time you look at them. So there are ‘orders’ or ‘levels’ of change, described by the number of levels of description required to get to the point where the pattern is invariant.
Your blood is constantly changing (systole, diastole), at this level of description there is no constant, because your blood pressure is constantly changing (lucky for us, or we’d be dead!). But at a higher level of description you get a pattern (high pressure, then lower pressure), that is invariant. You don’t get a systole and then another systole, or a succession of diastoles; they alternate. But this alternation is not constant either! The extent of the systole/diastole is ALSO constantly varying (also lucky for us, because this change, linked to what is known as ‘heart rate variability’, is strongly correlated with heart health), so it requires ANOTHER level of description to see how that is changing… and so on. At each level something ‘stays the same’ while other things ‘constantly change’. When we talk about change and constancy we have to be careful because we can never fully isolate one from the other; they are completely intertwined ‘all the way up and all the way down’.