# tixy.land

Yesterday I discovered this tweet from Martin Kleppe, which introduces the **tixy.land** website:

The idea is quite fun: basically, you can write a math expression that depends only on 4 variables (t,i,x,y) (hence the name of the web page), and the expression is rendered as animated dots located on a 16x16 grid, by applying simple rendering rules. Like this (example taken from the website):

The goal is then to provide a math expression that renders the “best” possible animation. And as the expression can be encoded directly in the URL, you can share it with others.

That’s pretty cool!

A lot of people actually replied to the initial tweet with examples of expressions that has become more and more complex in the evening. The expression given by the user is actually written in Javascript. I know almost nothing about Javascript, but I guess complex mini-programs can be written as math expressions. The site tells us that the expressions are limited to 32 chars, but that’s true only when you enter them on the text input form provided on the website. You can cheat a bit if you encode the expression directly in the URL.

The idea pleased me a lot, and I decided to give a try. To make my tests easier, I’ve recoded a G’MIC command that renders the same kind of animation than the **tixy.land** website. This command is usable from the CLI interface `gmic`

of G’MIC, and should be available after a stdlib update, if you use G’MIC 2.9.0+ (so `$ gmic up`

and you’re ready).

The command allows you to save a `.avi`

file corresponding to the animation, and is able to export the specified expression directly as a **tixy.land** URL.

That’s useful to test math expressions locally, without having to test directly on the **tixy.land** website. The grammar is not exactly the same, as here, I use the G’MIC math parser to evaluate the expressions, but it’s really not so different than what I’ve seen in Javascript so far.

# My first attempt:

I wanted to do something quite complex, so I didn’t try to respect the 32 chars limit.

What I did is take the `heart`

binary shape (G’MIC command `shape_heart`

), resized it to 16x16 and applied the DCT.

Then I filtered the DCT coefficients to keep only those with a high magnitude. As a result, I got an analytic expression, as a sum of weighted cosines, which renders an approximation of the heart binary shape. I finally added the (allowed) time variable `t`

in some of the cosines (those with the lowest coefficients), to generate an animation of a beating heart.

Here is the expression I ended up with:

```
expr = cos(0.4*x-0.2)+0.3*cos(0.8*x-0.4)-cos(0.2*y-0.1)-0.7*cos(0.4*x-0.2)*cos(0.2*y-0.1)+0.7*cos(0.8*x-0.4)*cos(0.2*y-0.1)+1.7*cos(0.4*y-0.2)-0.3*cos(0.4*x-0.2+3*t)*cos(0.4*y-0.2-t)+0.7*cos(0.6*y-0.3)+0.6*cos(0.4*x-0.2)*cos(0.6*y-0.3)+0.3*cos(0.8*x-0.4+t)*cos(0.6*y-0.3)+0.5*cos(0.8*y-0.4)+0.3*cos(1.2*x-0.6)*cos(0.8*y-0.4)+0.4*cos(y-0.5)-0.5*cos(0.8*x-0.4)*cos(y-0.5)-0.3*cos(1.6*x-0.8)*cos(1.2*y-0.6)-0.3*cos(0.8*x-0.4)*cos(1.6*y-0.8)
```

And here is the resulting animation:

What is nice is that you can see the same animation by visiting the following URL, redirecting to the **tixy.land** website:

That’s all for now, but I’m sure I will give another try in the future.

And you, what would you be able to achieve ?