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Mathematicians discover prime number pattern in fractal chaos
- baruchel 1y agoWithout paywall: https://www.removepaywall.com/search?url=https://www.scientificamerican.com/article/mathematicians-discover-prime-number-pattern-in-fractal-chaos/ https://www.removepaywall.com/search?url=https://www.scienti...
- deleted 1y ago[deleted]
- _ache_ 1y agoThe conference in question: https://www.youtube.com/watch?v=suFspoY3bBU https://www.youtube.com/watch?v=suFspoY3bBU The article is a good "first introduction" to the presentation.
- teekert 1y agoThat image at the top is eerily like Romanesco. I actually thought it was at first, but it's synthetic if you look at the left part (... or is it?). [0] https://duckduckgo.com/?q=Romanesco&iar=images&t=ffab&iai=https%3A%2F%2F4seasonsvegiefarm.com%2Fwp-content%2Fuploads%2F2015%2F05%2Fromanesco.jpg https://duckduckgo.com/?q=Romanesco&iar=images&t=ffab&iai=ht...
- danwills 1y agoI think that actually is a photo of Romanesco or at least a pretty good fake!
- ofalkaed 1y agoThe photo's attribution gives you all you need to know. https://www.gettyimages.com/detail/photo/romanesco-broccoli-close-up-royalty-free-image/185323744?adppopup=true https://www.gettyimages.com/detail/photo/romanesco-broccoli-...
- teekert 1y agoSince the left is so distant, I couldn't believe it was real. But it seems to be indeed. Very nice image.
- Sharlin 1y agoI don't think it's distant? The buds are just physically smaller there.
- p0w3n3d 1y agothe fractal broccoli blows my mind.
- JKCalhoun 1y agoFibonacci broccoli.
- RansomStark 1y agoDoodling in math class (vi hart): https://m.youtube.com/watch?v=bY1sOzTLrQQ https://m.youtube.com/watch?v=bY1sOzTLrQQ
- p0w3n3d 1y agoevery plant is a fibonacci plant because of leaves
- YcYc10 1y agoIt is broccoli.
- teekert 1y agoYeah it's also called Romanesco-Broccoli. Normal Broccoli is like this [0] [0] https://duckduckgo.com/?q=broccoli&t=ffab&ia=images&iax=images https://duckduckgo.com/?q=broccoli&t=ffab&ia=images&iax=imag...
- sva_ 1y agoInterestingly, you can often find fractal-like structures in nature as it is the result of maximizing surface area (to absorp sunlight) while minimizing space and energy used. Indeed, you can find an approximation to the (logarithmic) golden spiral in a romanesco, as each spiral arm is about the ratio of the Fibonacci sequence.
- Sharlin 1y agoIt's also one of the simplest possible shapes to encode, repeating the two basic instructions "grow" and "branch" independent of where in the plant you are.
- ndsipa_pomu 1y agoI would have bet a sizable amount of money (maybe 50 english pence) that the picture was of a Romanesco. They're one of my favourite vegetables though not commonly found in supermarkets round my way.
- ReptileMan 1y ago>In other words, just as a cloud of gas particles could be described deterministically if a powerful enough computer existed Let them try it with hydrogen gas.
- Quarrel 1y agoOk, I'll bite. Why? Isn't it still "just" a powerful enough computer?
- ReptileMan 1y agoHydrogen is small enough that uncertainty principle is not completely irrelevant.
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- danwills 1y agoI want to know more about an intuitive take on how the Zeta function does what it does! I know it must relate somehow to finding (or perhaps excluding) all the composite numbers but I'd really love to get more of a feeling about what each 'octave' of the function is adding-in. Seems like it must be something that 'flattens' the composites but increases sharply (in the infinite sum) at each prime.. but it's still a mystery to me how one could intuitively realise or discover that it's this specific function!? How did he do it?!
- dpflan 1y agoIs there a visualization possible of this pattern? For some reason this made me think of the Ulam Spiral -- https://en.wikipedia.org/wiki/Ulam_spiral https://en.wikipedia.org/wiki/Ulam_spiral.
- dkural 1y agoIt is unrelated to Ulam Spiral. The patterns there are due to various quadratic polynomials generating a finite number of primes, an observation going back to at least the time of Euler.
- zenethian 1y agoI wonder, has anyone tried looking for the pattern for prime numbers in a non-base-10 representation? I've always had a hunch that maybe the chaos only seems random because our representation of numbers could be misaligned with the pattern.
- mmargenot 1y agoThe patterns associated with primes are inherent to the numbers themselves and not their representations. The numbers are the pattern.
- psychoslave 1y agoYes. Also in practice we work with number representations, not number themselves. So there are some patterns where the representation is influenced by which base we encode them into. That's not something specific to primes of course. For example, length in term of digits or equivalently weight in bits will carry depending on the base, or more generally which encoding system is retained. Most encoding though require to specifically also transmit the convention at some point. Primes on the other hand, are supposedly already accessible from anywhere in the universe. Probably that's part of what make them so fascinating.
- bArray 1y agoYou can test it quite easily, but base doesn't seem to make a difference. There are some patterns that emerge when considering the primes spatially, though.
- alganet 1y agoWhat patterns emerge when you represent primes spatially?
- kevindamm 1y agoElsewhere someone already mentioned the Ulam Spiral [1] and I'll add the Sieve of Pritchard [2] which combines the Sieve of Eratosthenes with Wheel Factorization. Its wiki page has a nice visualization. Notice that when the primes are arranged in a rectangular grid (rows at a time, left-to-right, top-to-bottom) there are entire columns that can immediately be eliminated from consideration. [1]: https://wikipedia.org/wiki/Ulam_spiral https://wikipedia.org/wiki/Ulam_spiral [2]: https://wikipedia.org/wiki/Sieve_of_Pritchard https://wikipedia.org/wiki/Sieve_of_Pritchard
- afpx 1y agoNot that I understand all of this. But does that mean a bijection exists from probability values to specific prime positions?
- dkural 1y agoNo, not at all. A bijection is a very strong requirement. There is no kind of morphism of any kind here, between any given prime and a probability, just an estimate of prime density.
- DougN7 1y agoDoes this have any implications for cryptography where factoring to find large primes is involved?
- dkural 1y agoNo, it doesn't - here's an easy way to see why: You can already assume any conjecture to be true to see if it helps you factor a large number. After all it's easy to check your answer.
- profsummergig 1y agoLooking for (possibly accidental) patterns. The obsession with prime numbers (humans decided they were "prime", i.e. most important, based on arbitrary considerations). It seems like a version of astrology to me. Am I wrong? I'd be happy to be proved wrong.
- eapriv 1y agoYou are wrong. Prime numbers are fundamental to mathematics.
- mjyh 1y agoThe property of certain input numbers being "prime" is required for RSA key generation.
- a57721 1y ago> humans decided they were "prime", i.e. most important, based on arbitrary considerations No, not arbitrary considerations. The term goes back at least to Euclid who investigated factorization of integers in his "Elements". He used the greek word "protos" that was later translated to Latin as "primus". It doesn't mean "most important", rather "first". The idea is that primes are the "multiplicative building blocks" for other numbers, the "origin" or "first principles", because every integer factors into primes. When a mathematical object can be decomposed in some way, it is very natural to study the irreducible blocks, because many questions boil down to them.
- stevefan1999 1y agoPrime numbers are also important in computability theory. Godel number, for example, uses prime number to assign each symbol and laid the foundation for Godel's incompleteness theorem
- _aobj 1y ago[dead]