Making Mathematical Art with L-Systems

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  • čas přidán 30. 05. 2024
  • Tom Rocks Maths intern Max Cairney-Leeming explains how to make mathematical art using Lindenmayer Systems...
    L-systems consist of lists of symbols which represent a drawing function, and a set of rules that are applied to the symbols iteratively. Starting from a simple axiom - often just a straight line - complex systems can be generated which demonstrate fractal-like behaviour. The Heighway Dragon Curve is one such example, as well as realistic plants and trees that are used in animations in films and video games.
    Produced by Max Cairney-Leeming with assistance from Dr Tom Crawford. Max is a second year student studying Maths and Computer Science at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac.uk/people/tom-c...
    For more maths content check out Tom's website tomrocksmaths.com/
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    Thank you to the following for providing images/video clips under a Creative Commons licence:
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    Icecreeper28
    Ryoichi Mizuno
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Komentáře • 47

  • @TomRocksMaths
    @TomRocksMaths  Před 3 lety +16

    Check out Max's video explaining how to 3D print your own fractal here: czcams.com/video/yMgaobj3Edw/video.html

    • @wgwells
      @wgwells Před 2 lety

      I wondered why Tom's voice had dropped to a lower register! XD

  • @travisgray6983
    @travisgray6983 Před 2 lety +14

    Wow, I'm impressed with how natural some of those botanical inspired systems look. It's amazing what patterns and shapes emerge from such simple sets of rules!

    • @stevecummins324
      @stevecummins324 Před 2 lety

      Going the other direction... I recommend a book by the Biologist Brian Goodwyn "how the leopard changed its spots"... covered how simple properties relating to say calcium concentration, and membrane "springyness" could be responsible for much of the morphology of biology. Also seems able to explain pigmentation patterns in say cats... hence the title. lol

  • @dragoncurveenthusiast
    @dragoncurveenthusiast Před 2 lety +9

    I love these kinds of things

  • @CompleteGodel
    @CompleteGodel Před 10 dny

    Great video! Just found out cinema4d allows L-systems to be easily implemented in 3d, and this helped a lot.

  • @Brontalo
    @Brontalo Před rokem +2

    An L-system i found is:
    A = -C++A ; B = B--C+ ; C = AB with Axiom AB.
    A,B,C is just draw 1 forward and +,- is turn 45°.
    and it turns into a neat wave-spiral.

  • @robertschlesinger1342
    @robertschlesinger1342 Před 2 lety +5

    Very interesting and worthwhile video. An excellent book on the subject is "The Algorithmic Beauty of Plants."

  • @Nhn1460
    @Nhn1460 Před 2 lety +3

    I did a paper in my ib on the fibonacci fractal and its similar to this with the rule Fn => Fn-1 + Fn-2 but rather than adding numbers it puts together 0s and 1s which decide its direction. Really interesting to see a video on a similar system!

  • @srinandanasastry3001
    @srinandanasastry3001 Před 2 lety +4

    You always come up with some really legit stuff 🤩💫

  • @NateCrownwell
    @NateCrownwell Před 2 lety +1

    Super cool! Thank you Tom!

  • @henrymarkson3758
    @henrymarkson3758 Před 2 lety +3

    Great stuff, Max.

  • @DommageCollateral
    @DommageCollateral Před 11 měsíci +1

    0:43 i would call it alphabet and letters (or how do you engl call alphabet elements?). this is basically just a way of creating the syntax for predicate logik

  • @jameshyde830
    @jameshyde830 Před 2 lety +1

    This takes me back 13 years!

    • @TomRocksMaths
      @TomRocksMaths  Před 2 lety

      Was this part of the CS course?

    • @jameshyde830
      @jameshyde830 Před 2 lety +3

      @@TomRocksMaths yeah it was one of the two assignments in Michaelmas, using Haskell.

  • @joshuaisemperor
    @joshuaisemperor Před 2 lety +2

    Cool!

  • @bludeat7398
    @bludeat7398 Před 3 lety +4

    nice

  • @janjaki2741
    @janjaki2741 Před 2 lety +2

    I think im going to use these for my art very soon 😍

  • @tjtommy5495
    @tjtommy5495 Před rokem

    How would you go about making a Penrose Tiling using L Systems?

  • @HienNguyenHMN
    @HienNguyenHMN Před 2 lety +1

    I wonder if there's a way to introduce chance. e.g., sometimes a branch ends in a leaf and sometimes it continues to spawn new branches/trunks.

    • @TomRocksMaths
      @TomRocksMaths  Před 2 lety +2

      yes - these kinds of models are used for the growth of trees and networks of blood vessels in the body

  • @kadeksatriadi7845
    @kadeksatriadi7845 Před 2 lety +1

    I am inspired!

  • @Reliquancy
    @Reliquancy Před 2 lety +1

    I was thinking maybe there’s a way to translate the axioms of geometry into an l system so for example the pons asinorum theorem looks like a shrub maybe idk.

  • @conorgardiner3081
    @conorgardiner3081 Před 2 lety +2

    Love ur vids where u do schools exams👍 could you do a national 5 Scottish exam please. Keep it up 🙌

    • @TomRocksMaths
      @TomRocksMaths  Před 2 lety +1

      I'll add it to the list thanks - more exam videos coming over the summer.

  • @mathevengers1131
    @mathevengers1131 Před 3 lety

    Here's link to a video of fractional calculus:
    czcams.com/video/yI6GAWcrKfY/video.html

  • @sakibhasan7857
    @sakibhasan7857 Před 2 lety +3

    Is that ur voice?

    • @ragnkja
      @ragnkja Před 2 lety +5

      The voice in the video is that of Max Cairney-Leeming.

  • @ralluzarebon
    @ralluzarebon Před 3 měsíci

    Kshars lvl

  • @leeme7513
    @leeme7513 Před 2 lety +1

    would you take an IQ test and show your results?

    • @TomRocksMaths
      @TomRocksMaths  Před 2 lety +1

      I don't really believe in IQ tests - they are just like any other exam and can be studied for

    • @stevecummins324
      @stevecummins324 Před 2 lety

      they're testing something, but I fairly sure it's not intelligence
      I used to be fairly rubbish at the multiple choice visual, spot the pattern type.. Had a hunch they might work similar to Stroop tests and be more about confidence/lack of cognitive interference/not 2nd guessing oneself etc than IQ. On computer biased implementation, when I changed technique and stopped trying to actively reason the patterns, and had confidence to button bash, sticking with the very first answer that I felt like...I tend to score +20 over my original technique.. Not being able to justify choice of answers with more than "it felt right" ... well that doesn't sit well with my understanding of what IQ should mean lol

  • @77tigers26
    @77tigers26 Před 2 lety +1

    nice