Elm – fun with L-System (Part 3)

You can become a serverless blackbelt. Enrol to my 4-week online workshop Production-Ready Serverless and gain hands-on experience building something from scratch using serverless technologies. At the end of the workshop, you should have a broader view of the challenges you will face as your serverless architecture matures and expands. You should also have a firm grasp on when serverless is a good fit for your system as well as common pitfalls you need to avoid. Sign up now and get 15% discount with the code yanprs15!


  1. Algae
  2. Pythagoras Tree
  3. Cantor Dust (this)
  4. Koch Curve
  5. Sierpinski Triangle
  6. Dragon Curve
  7. Fractal Plant

Last time out we implemented the Pythagoras Tree example from the L-System wikipedia page. Now, let’s continue our journey and see how we can implement the Cantor Dust example in Elm.

Example 3 : Cantor Dust

First, let’s define our L-System:


The interesting thing about this example is that we need to draw, not only the current generation, but also all the preceding generations too.

So I had to approach things slightly differently, and instead of dealing with a Signal(State), I need a Signal(List(State)):


This signal of List(State) is then passed to the display function (along with the dimension of the window):



We can use rectangle to represent the individual bars, and for my screen 25 pixels seems to be a good height.


For each generation we want to place them some distance apart. That is to say that the state for each generation should have a stepped Y position.


so now, we need to add a drawState function that will take in:

  • the width of the window;
  • the y position for its rectangles; and
  • the state it needs to draw

and return a list of rectangles for that state.


You may remember the following paragraph from Part 2:


So to work out the x positions of the first rectangle for this state, we have this slightly dubious looking line of code:



and the next block of code generates the x positions for all the rectangles:



Running this example in Elm Reactor I can get the demo to gen 8, after that it takes noticeably longer to render and the bars are so thin that they’re barely visible.



Live Demo (here)

Use LEFT and RIGHT arrow keys to evolve/devolve the L-System.


Source Code (here)


Next : Koch Curve


Liked this article? Support me on Patreon and get direct help from me via a private Slack channel or 1-2-1 mentoring.
Subscribe to my newsletter

Hi, I’m Yan. I’m an AWS Serverless Hero and the author of Production-Ready Serverless.

I specialise in rapidly transitioning teams to serverless and building production-ready services on AWS.

Are you struggling with serverless or need guidance on best practices? Do you want someone to review your architecture and help you avoid costly mistakes down the line? Whatever the case, I’m here to help.

Hire me.

Check out my new podcast Real-World Serverless where I talk with engineers who are building amazing things with serverless technologies and discuss the real-world use cases and challenges they face. If you’re interested in what people are actually doing with serverless and what it’s really like to be working with serverless day-to-day, then this is the podcast for you.

Check out my new course, Learn you some Lambda best practice for great good! In this course, you will learn best practices for working with AWS Lambda in terms of performance, cost, security, scalability, resilience and observability. We will also cover latest features from re:Invent 2019 such as Provisioned Concurrency and Lambda Destinations. Enrol now and start learning!

Check out my video course, Complete Guide to AWS Step Functions. In this course, we’ll cover everything you need to know to use AWS Step Functions service effectively. There is something for everyone from beginners to more advanced users looking for design patterns and best practices. Enrol now and start learning!

Are you working with Serverless and looking for expert training to level-up your skills? Or are you looking for a solid foundation to start from? Look no further, register for my Production-Ready Serverless workshop to learn how to build production-grade Serverless applications!

Find a workshop near you