The Hidden Structure of Rule 30

Comments · 517

• ER

  @EricRowland · 1 month ago · pinned

  Bonus video on Patreon! <a href="https://www.patreon.com/EricRowland/posts/rule-30-bonus-166690946">https://www.patreon.com/EricRowland/posts/rule-30-bonus-166690946</a><br>There are many cellular automaton rules with the same property as Rule 30. We&apos;ll see several in this bonus video. It&apos;s free to watch on Patreon.

  32

• EL

  @elizathegamer413 · 1 month ago

  I fear the 34th rule universe

  791

• ZA

  @zaffyr · 1 month ago

  That moment when the infinite void to the left turned out to be just another black triangle, was genuinely mind blowing

  251

• QU

  @quantum411 · 1 month ago (edited)

  My mum has a knitted scarf with the Rule 30 pattern on it. It has always fascinated me.

  119

• SP

  @spitsmuis4772 · 1 month ago

  I feel like most of the 256 rules don&apos;t even get the chance to show their potential complexity, because of the apparent need to start with one square

  170

• SD

  @SDS_Alex · 1 month ago

  That line where order becomes chaos makes me think of the critical brain hypothesis.

  24

• BO

  @boing7679 · 1 month ago

  I&apos;m way too sleepy to understand most of this but I love the animations and all

  56

• CO

  @colinbrown7947 · 1 month ago

  <a href="https://www.youtube.com/watch?v=HcGjCcLEgN4&amp;t=1072">17:52</a> just had to pause and think. Wow thats amazing.

  17

• GO

  @GoodTheta · 1 month ago

  $30,000 for all three -- there I was thinking I&apos;d get paid <i>less</i> for solving all three at once.

  17

• TE

  @terdragontra8900 · 1 month ago

  <a href="https://www.youtube.com/watch?v=HcGjCcLEgN4&amp;t=1012">16:52</a> Ive been fascinated by the sequence 1,2,1,3,1,2,1,4 etc. since 6th grade, ah, how nostalgic. I realized a while ago that it’s weird when you want to extend it backwards (the “0th” term should be infinity, then going backwards further gives the same sequence as going forwards) Cool to see that visually reflected here with this sequence which is a weirdly distorted version of it.

  66

• MR

  @MrAfrojoe89 · 13 days ago

  Love your stuff man!<br> &nbsp; Ima fan!😊

  1

• TR

  @Tremeschin · 1 month ago (edited)

  All my body was screaming Collatz Conjecture this whole video, a similar periodic left pattern is seen when you plot whichever branch of even/odd rule was applied to a given number as 1s and 0s (blue and black) in the shear visualization form (chaotic, but deterministic), with organized chaos on the right, and infinitely palindrome 1314131 branch counts everywhere! (more evident starting at powers of two, or flipping it diagonally so the k-th column of a line n is the n-th branch for the k-th number)<br><br>There seems to exist fundamental space-filling generator sequences that describe these fractal structures when stable, wouldn&apos;t be surprised if some automaton (perhaps rule 30 itself) is tightly related to it, or maybe reframing collatz as one have a match. A small detail, the right side void needs to be an infinite 01 sequence (4, 2, 1) in simplified form (x/2) and (3x+1)/2 for a potential &apos;must end here&apos;&apos; proof :)<br><br>Also, I wonder how all these relate to 2 or 3-adic numbers (similar organized vs pure chaos frontiers, and sierpinski triangles showing up in other automatons). When playing with it, numbers seemed to have a 1:1 mapping with a &apos;random&apos;, but deterministic and unique choice route to reach them, a binary or ternary (groups) encoding of some sort.<br><br>(ps. I&apos;m just a programmer and engineer that likes maths for fun, this could all be known as the field is huge haha)

  11