from Hacker News

Mathematicians Have Found a Shape with a Pattern That Never Repeats

by rfreytag on 6/22/23, 3:03 AM with 43 comments

  • by saint_abroad on 6/23/23, 1:52 PM

    2 months later we have the "Spectre" - an aperiodic monotile (without reflections): https://aperiodical.com/2023/05/now-thats-what-i-call-an-ape...

    Edit - a visual explanation of this journey: https://www.youtube.com/watch?v=IfVwelta1fE

  • by jossclimb on 6/23/23, 2:49 PM

    This is not mentioned until half way through, but I find fascinating..

    > David Smith, a retired printing technician and nonprofessional mathematician, was the first to come up with the shape that could be a solution to the long-standing “einstein problem.” He shared his ideas with scientists who took on the challenge of trying to mathematically prove his conjecture

  • by samwillis on 6/23/23, 2:07 PM

    Significant previous discussion: https://news.ycombinator.com/item?id=35273707

    Mathematicians discover shape that can tile a wall and never repeat (newscientist.com) - 488 points, 3 months ago, 160 comments

  • by once_inc on 6/23/23, 1:56 PM

    This was found months ago, no? I saw several articles about the Einstein back then.

  • by andrethegiant on 6/23/23, 1:56 PM

    Oh shit new shape just dropped

  • by roberthahn on 6/23/23, 2:36 PM

    I would be very interested in seeing what definition of “pattern” this discovery is using.

    Most definitions I could find (I am not a mathematician) seems to imply one of: repetition, growth or shirking.

    This shape appears to have none of these properties but they still call it a pattern.

  • by Maxion on 6/23/23, 2:07 PM

    I guess this means that I now should re-tile my bathroom. hmm.

  • by forkerenok on 6/23/23, 2:04 PM

    I still maintain this naive belief that all of math is elegant, and from that perspective 13 sides sounds and looks oddly specific and feels contrived to me, at least without knowing specificities of the field.

    Where do 13 sides come from? Is it related to a number of transformations?

  • by kfrzcode on 6/23/23, 2:34 PM

    I don't get it. The first image I can clearly see patterns of triangular arrangements. What does this news actually mean

  • by youssefabdelm on 6/23/23, 2:18 PM

    Lol it repeats alright... blah blah blah "it doesn't technically repeat"... To the brain it does, it's like white noise. If I showed you an evolving animation of this shit for 3 hours it would be torture. Someone should measure something like the multiscale entropy of this pattern.

    Edit: I will say the coolest thing about this is the cross-disciplinary connection hints at a metapattern: https://youtu.be/48sCx-wBs34?t=1007