Elm – fun with L-System (Part 3)

Series:

  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:

image

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)):

image

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

image

 

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

image

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.

image

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.

image

You may remember the following paragraph from Part 2:

image

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

image

image

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

image

 

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.

image

 

Live Demo (here)

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

 

Source Code (here)

 

Next : Koch Curve

Links

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 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. Including basic concepts, HTTP and event triggers, activities, callbacks, nested workflows, design patterns and best practices.

Get Your Copy