Elm – fun with L-System (Part 3)

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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

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