> I would like to understand why numbers looks like leaves
1st of all they don't. The graph doesn't look like pinnatids or palmatids. There is some resemblance of an alternating disposition of leaves, but that's not the shape of the leaf itself but the distribution of them, and it's a stretch.
Secondly, I'll take the generous interpretation of the question which is, why the graph looks mathematically like leaves, and not a question of biological impact, whatever resemblance is a coincidence which brings us to
Third, OP is playing a game with numbers with no objective goal (yes all maths is this, but this is straight up chmess), there is no ultimate meaning to be derived of it.
I think the last point doesn't really hold its own in any way. Many discoveries throughout history have started from someone just playing around with an idea, toying with it at first, but eventually becoming obsessed. The thing is, there's no way to tell beforehand. It might be a toy with no ultimate use or meaning, or it might lead to something entirely novel somewhere down the line. That's why play, in a very broad sense, is a core part of science and invention.
It sounds like you have an infallible instinct for exactly which lines of research should be funded and which are useless dead ends. The NSF should hire you immediately!
But he's not wrong, research really isn't just random playing (which I think is obviously still good and fun and should be done for it's own sake, of which this blog post is a great example though it probably wouldn't be worth the time of a formal research project).
It's the reason why "good questions" and seemingly arbitrary or trivial problems - especially those which motivates the development of much deeper machinery or discovery in order to solve them - is widely appreciated across all fields of math (poincare conjecture, galoi's proof of the unsolvability of the quintic, fermat's last theorem, riemann zeta's zeroes etc.)
In all cases those good questions where not randomly cooked up but posed from a previous, more direct line of inquiry, of which the originator usually had a good insight into. Though for the examples I gave the unexpected depth certainly could not have been anticipated beforehand.
always the problem with scientific research is that we never know why anything actually works the way it does, but we have a lot of ways of talking about it
1st of all they don't. The graph doesn't look like pinnatids or palmatids. There is some resemblance of an alternating disposition of leaves, but that's not the shape of the leaf itself but the distribution of them, and it's a stretch.
Secondly, I'll take the generous interpretation of the question which is, why the graph looks mathematically like leaves, and not a question of biological impact, whatever resemblance is a coincidence which brings us to
Third, OP is playing a game with numbers with no objective goal (yes all maths is this, but this is straight up chmess), there is no ultimate meaning to be derived of it.