Making Mathematical Art with L-Systems

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...
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Thank you to the following for providing images/video clips under a Creative Commons licence:
Schmendreck
Icecreeper28
Ryoichi Mizuno
Confreaks

[@TomRocksMaths]

Check out Max's video explaining how to 3D print your own fractal here: kzbin.info/www/bejne/r37KkqKYn5h4mtk

[@wgwells]

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

[@travisgray6983]

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]

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]

I love these kinds of things

[@TomRocksMaths]

The name kinda gives it away :p

[@CompleteGodel]

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

[@Brontalo]

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.

[@TomRocksMaths]

awesome :)

[@robertschlesinger1342]

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

[@TomRocksMaths]

Yes - great book.

[@Enigma758]

I have two copies 😃

[@Nhn1460]

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]

You always come up with some really legit stuff 🤩💫

[@TomRocksMaths]

Glad you enjoyed it!

[@NateCrownwell]

Super cool! Thank you Tom!

[@TomRocksMaths]

Glad you enjoyed it :)

[@henrymarkson3758]

Great stuff, Max.

[@TomRocksMaths]

Agreed!!

[@DommageCollateral]

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]

This takes me back 13 years!

[@TomRocksMaths]

Was this part of the CS course?

[@jameshyde830]

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

[@joshuaisemperor]

Cool!

[@bludeat7398]

nice

[@janjaki2741]

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

[@TomRocksMaths]

awesome - let me know how they turn out!

[@tjtommy5495]

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

[@HienNguyenHMN]

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]

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

[@kadeksatriadi7845]

I am inspired!

[@TomRocksMaths]

awesome!

[@Reliquancy]

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.

[@TomRocksMaths]

A fun idea for sure!

[@conorgardiner3081]

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

[@TomRocksMaths]

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

[@mathevengers1131]

Here's link to a video of fractional calculus: kzbin.info/www/bejne/r3qZeHSNmNd-nLs

[@sakibhasan7857]

Is that ur voice?

[@ragnkja]

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

[@ralluzarebon]

Kshars lvl

[@leeme7513]

would you take an IQ test and show your results?

[@TomRocksMaths]

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

[@stevecummins324]

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]

nice

[@TomRocksMaths]

glad you enjoyed it!