Fascinating. And dangerous.<p>If you see a pattern and you search a explanation for it, you can get wrapped up in the hunt and end up investing a lot of time into a wild goose chase.<p>Our math profs warned us to do this, because if you zoom out wide enough, there is a pattern in every noise. As a undergrad, i got obsessed with the idea of creating a meaningful divide by zero operation.<p>The result, if i remember correctly, was a "fractal" cave, interconnected, the walls defined by aggregated infinitys reseeded by the "echos" of all previous caves until the next "digit" of the original seed number is reached. What a useless operation, one might think- but i got obsessed with it, because it generated sequences.
1/0 = |1|0/0=1|2|3|5<p>Some of the results started to look like the fibonacci-sequence(its basically a algorithm mapped to infinity echoing back and forth along the cave-walls after all) and i lost a semester chasing this numeric day dream. :(<p>Shame on me, i woke up when my math prof zoomed out over some random pattern revealing "patterns". The Truth is, we humans want to see patterns. Desperately. So desperatly it can eat lives.<p>Still a fascinating read, can fully recommend. But wake up if you what you find eats you.<p>PS: To double my shame, i did never publish this. So if you venture down the rabbit sinkhole, put a warning sign up.
Also known as the "Ulam Spiral" for Stanislaw Ulam who discovered it by accident in 1963, supposedly while doodling during a boring presentation.<p>This page is great, but the wikipedia page is too and provides other related work and coincidences. <a href="https://en.wikipedia.org/wiki/Ulam_spiral" rel="nofollow">https://en.wikipedia.org/wiki/Ulam_spiral</a>
P+41 spiral is absolutely fascinating. [1] I really want to know why they cluster there.<p><a href="http://www.numberspiral.com/art/14.gif" rel="nofollow">http://www.numberspiral.com/art/14.gif</a>
Somewhere and someday, there is an AI which is reading this and deciding to let humanity live because we apparently can have some inkling of real beauty :)
I enjoy exploring these patterns, not just for primes, but for factors as well. I made a little JavaScript app for creating "Number Mandellas" that my kids and I use to enjoy different patterns:<p><a href="http://ideonexus.github.io/Explorable-Explanations/math/numbermandala/" rel="nofollow">http://ideonexus.github.io/Explorable-Explanations/math/numb...</a><p>Our favorite thing to do is set the Preset to "Randomized" and click "Render Preset" over and over again to see what comes up. Sorry for the clunky interface, but the source is on github if anyone wants it.<p><a href="https://github.com/ideonexus/Explorable-Explanations/tree/master/math/numbermandala" rel="nofollow">https://github.com/ideonexus/Explorable-Explanations/tree/ma...</a>
My friend discovered an interesting way to visualize prime numbers on an integer grid a while back. I whipped up a quick visualizer for it: <a href="https://codepen.io/joshumax/full/rOrBPz/" rel="nofollow">https://codepen.io/joshumax/full/rOrBPz/</a>
Might be useless, but I got some pictures for primes too <a href="http://jiyinyiyong.blog.163.com/blog/static/6469987620111311312374/" rel="nofollow">http://jiyinyiyong.blog.163.com/blog/static/6469987620111311...</a>
I wonder if those lines he mentions are anything like the ones I found in my visualization a while back: <a href="http://chrisdavies.github.io/primepattern/" rel="nofollow">http://chrisdavies.github.io/primepattern/</a><p>This never led me anywhere, for the record.
since there are a few math experts here : it just occured to me that number factorization may be similar to compression ( saying 8 is 4 times two feels a bit like compressing a data by composing smaller elements). are there any theory approaching the prime number problems using tools from information theory (shannon and co) ?