Elm, Eikonal, and Sol LeWitt

We saw this cool Sol LeWitt wall at MASS MoCA. It did not escape our attention that it was basically an eikonal equation and that the weird junctures were caustic lines.

It was drawn with alternating colored marker lines appearing a cm away from the previous line. This is basically Huygens principal.

So I hacked together a demo in elm. Elm is a Haskell-ish language for the web.

 

 

 

So I made a quick rip and run elm program to do this. This is the output, which I could make more dynamic.

The algorithm is to turn a list of points into their connecting lines. Then move the line perpendicular to itself, then recompute the new intersection points. It’s somewhat reminiscent of Verlet integration. Lines coordinates are momentum-like and points are position like and we alternate them. This is a finite difference version of the geometric Huygen’s principle.

Alternative methods which might work better include the Fast Marching Method or just using the wave equation and then plotting iso surfaces.

I also had to resample the function to get only the maximum y value for each x value in order to duplicate the LeWitt effect.

sol

These are the helper functions with lots of junk in there

And this is the svg main program.

 

 

notes on elm

elm is installed with npm

elm-repl

you import packages (including your own) with

import ThisPackage

and you check types by just writing them and hitting enter rather than :t

elm-live is a very handy thing. A live reloading server that watches for changes in your files.

elm-make myfile.elm

will generate the javascript and html

This is a good tutorial and a good snippet to get you going

 

Differences from Haskell:

elm isn’t lazy which is probably good.

The composition operator (.) is now <<

elm doesn’t have the multiline pattern match of haskell. You need  to use case expressions. I miss them.

typeclass facilities are not emphasized.

The list type is List a rather than [a]