A mathematical rule this simple should not look this alive Thousands of Collatz trajectories are folded through symmetry and grow into something thats almost botanical... ordered, delicate and strangely natural. Nome of this proves the Collatz conjecture, of course, but it is striking to see so much structure come... from a problem that still resists proof. Maybe AI systems will crack this one.show more

The physicist in me sees a biased Brownian motion, a pseudo-random walk. ⦚⍼

Youre not wrong. I perturbed the trajectories with some Gaussian noise to get that natural look

f(z)_c = z^2+c

Mathematicians are having a moment and I’m here for it. 🤩

Any random blurb duplicated with mirror or rotational symmetries looks like "something" meaningful.

oh, this is VERY botanical...looks like the structure connecting every mushroom and tree on the planet..and thank you so much for the delicious music!

Symmetry emerging from pure number rules feels like nature hiding inside math itself

It's also one of those 3D visualisations whose apparent direction of rotation can be reversed by a change in perception.

yeah, but which way is it spining? 😁

The colatz conjecture is physics not linear algebra. It is 3(x,y,z)+1 but is 8nterpreted as a linear equation. So we see the 421 but the truth is a 3D model of bubble theory.

Whitehead tends to call working all the possibilities out and this form you see eternal objects. Is interesting if you do work out all the possible trajectories or whatever things end up looking like this bit like trees or crystals and such.

Beautiful! 🔥

no way this is solved .. i raped chatgpt's mind with ideas yet it kept going in circles .. the problem is solved approximately but you can never prove that a trajectory wont explode to infinity .. its also like a hash fuction .. technically cryptography would be dead if collatz

Strange how fundamental it is, isn’t it?

😲👏🏼 I don’t think I’ve ever seen a visualization of it

Those folded patterns look oddly like vines

Awareness is an aspect of the inorganic. This could be an example.

@Grok is this the expansion leg of the 7 energies that we have mapped in UNL?

Looking forward to the moment when the answer appears, it will be even more shocking

Looks like many species of flowers without singular petals.

@drmichaellevin

C'est une vision totalement arbitraire et évidemment fausse tant qu'on a pas découvert le lemme garantissant l'absorption pour chaque orbite

It might be that resisting proof is what gives it life. Solving things turns them into crystals generally.

There is NOTHING to be proven here !!! The Only proof there is , is that all is Growing and forever Evolving !!! NO Growth NO Evolving The Nature of the universe !!!

“The Shape of Returning.” An artistic imagining of Collatz: wandering paths gathering towards a shared home. A visual metaphor, rather than a calculated map.

Ancient ones craked it already ! "As above so below" Geometric pattern found in all natural systems Lungs, trees, rivers, vascular system Always the same

beautiful

Looks like pubes.

@grok explain this

I feel the proof itself seems insignificant. People revel in the process of the game rather than the result of the proof.

Nome, none, some

Made with AI prompted, with equations. 1-2 images are final product of a series the model went through to get there. The process is very interesting. 3-4 are the steps combined into transparent layers, this shows a lot. I think.

Who says it resists proof?

OEIS 00548D...