Explanation for similar structures at different scales

[Jimster41]

I hope this is the most appropriate place for this question...

So the PF posted this cool set of pictures yesterday on FB. Hopefully the link below works. It shows how some really big things "look" similar to some really small things.

https://www.facebook.com/physicsfor...0.1428253991./972230119477736/?type=1&theater

It's exactly the kind of thing that has been bugging me for awhile. Probably since reading Eric Chaisson's "The Life Era" a number of years ago.
https://www.amazon.com/dp/0595007910/?tag=pfamazon01-20
So I was excited to see it. But it made me think I'm missing out on a thread somewhere...

Q: Why (physically) do they look so similar?
I've entertained the following answers at least:

A: It's a philosophical and aesthetic question, inherently not about physics
My response: "Okay..."

A: They don't really look similar, it's a mirage of perspective. Change the conceptual angle from which you perceive them, and suddenly they look nothing at all alike
My response: "I see..."

A: Totally a coincidence, with a nearly infinite variety of shapes, you can always find two things that look surprisingly similar.
My response: I don't find this answer particularly convincing, though maybe I should. Seems like such a claim could be analyzed in some rough probabalistic way.

A: Because physical laws are the same everywhere.
My response: I get space and time invariance of physical laws but I guess I'm not clear on scale in-variance. The theoretical tools used in physics do seems to be scale specific (classical vs. Quantum, macroscopic vs. microscopic...)

A: The selection process at work in Quantum Mechanical Cosmic Evolution appears to manifest discrete scale in-variance.
My response: That would be neat but... what are you smoking by the way?

I've been thinking about Entropy w/respect to such things - a gross takeaway from various readings, initiated largely by Chaisson's postulates. But I understand Entropy better now - and realize that it is not the word most applicable. The right word is "Complexity". In a recent video I watched L. Susskind compared Complexity to Entropy w/respect to quantum mechanical things, how the complexity of a QM system does not scale llike it's entropy (I think that's what it was). I hadn't realized that. Got my attention. My motivation to understand why is high, plus, now Chaisson has a new book out that I just got.
https://www.amazon.com/dp/0674009878/?tag=pfamazon01-20
In it he references forthcoming work on making the analysis of complexity quantitative. Just curious where knowledgeable types come down on this, if at all? Whether or not there is a discussion happening somewhere.

 

[rootone]

The first answer is the one that comes to mind for me.
'Looks similar' is subjective, but you could find that on actually measuring similar looking things that that are not a similar as they first appear.
A lot of thing 'look like', a spiral let's say, but there are many things in Nature, both large and small, that fit the generic description 'spiral', whilst the mathematical and physical properties of one spiral structure can be shown to be very different to another.
On the other hand there are some kinds of structure which are very primitive concepts, such as a 'sphere'.
Spheres can be described in very simple math terms, and the physics of one sphere can be directly analagous to another sphere.
That doesn't seem to be surprising since simple structures are more likely to occur than complex ones.

 

[wabbit]

I think there are also complex structures generated by simple mechanisms - and mechanisms of a completely different physical nature (as in the case of these pictures) can share some traits so that they generate structures which look similar. I can only think of growth / branching mechanisms right now, which can apply at any scale and where the overall aspect of the result can depend on just a few parameters, regardless of what the specific underlying physical (or biological) mechanism is.

For some reason, the term "morphogenesis" seems to have been preempted by biology - but I think the ideas developped there go beyond that field.