I don't think Turing-completeness implies omniperiodicity. I'm imagining a cellular automaton which follows Game of Life rules on even-numbered generations and does nothing on odd-numbered generations, which is trivially Turing-complete because it's just Conway's Game of Life if you ignore every other generation, but also trivially has no odd-period oscillators.

That texture healing looks super nice. Is that something fonts can just do or does it require special editor support?

I might buy more from Epic if their launcher weren't So. Freaking. Slow. Even claiming the free game is such a chore that I can't be bothered to do it. It takes several minutes to load, responds sluggishly, and lags everything else on my computer the whole time it's running. The only game I play from them anymore is Celeste because I can start it without ever going through the launcher.

If you don't need to reuse the collection or access its items out of order, you can also use Iterable which accepts even more inputs like generators.

...What are they actually launching though? I mean I love the payment scheme but I can't get excited over this without an actual good product being sold.

The one case where I prefer video is when I know next to nothing about the topic and the other choice is mediocre to low-quality writing. Most people aren't great technical writers, and it's easy to skip over steps either because the writer assumes too much prior knowledge or simply because it takes effort to put that information in. On the other hand, videos are the opposite where it takes effort to cut stuff out, so you usually get all the steps which is what I need when I don't know anything.

If I have the option of a well-written, step-by-step tutorial though, or if I already know the topic and have a vague idea of what I'm looking for, then text is much better for being able to search/skim/go back and forth at my own pace.

No idea how hard it would be but it would be nice to have code blocks with syntax highlighting like on Github, so you could write something like

```python
def f(x):
    return x
```

and get *removed externally hosted image*

Do you care about modeling the cells? If not, you could represent each row with just a number. When X plays, add 1 to all the rows that include the position they played, and when O plays, subtract 1. If any row reaches +3 or -3, that player wins.

As for rotation/reflection invariance, that seems more like a math problem than a Rust problem.

Some clarifications: f(x) = -2x/3 + 5 isn't technically correct. It happens to equal that when x is between 6 and 9, but the function is different outside of that range. Similarly, your equation for F(x) is only correct when x is between 6 and 9. The reason this matters is because F(0) = 2 doesn't mean C = 2. That only works if the function is the same all the way to x = 0, which it's not.

If you want to solve by integrating, you would have to integrate each section and find the right C for each section that makes the integrals all connect to each other.

Alternatively, you can use the property that F(b) - F(a) = the area under f(x) from a to b. I think that region from x = 4 to 6 is supposed to be a semicircle, so each section is a standard shape and you can calculate the area using geometry.