1:09 PM
I've never seen this type of puzzle game before, but it seems very interesting:

2 hours later…
3:05 PM
@flawr That's pretty cool.

3:27 PM
@flawr I ignored this when I first saw it...but this is really cool
its really not about music though
its about cycles in base 12
oh wait.
The lines aren't consistent
:/
like, there's a diagonal line that goes Fb Ab C E
the one next to it goes Bb Db F A
the first diagonal line is all major thirds (and Fb and E are the same note)
the second starts with a minor third
then does major thirds
Ooooh...its a double flat. Nevermind. They need to write their double flats better :P
```   1   8   3   A
A   5   0   7   2
2   9   4   B
B   6   1   8   3
3   A   5   0
C   7   2   9   4
4   B   6   1```
Anyways, that's basically the pattern
you have +5 going east, +4 going south-east, +3 going north-east, and +1 going south

3:53 PM

2 hours later…
6:00 PM
Any ideas for interesting integral functions with (a) fixed point(s)? Asking for this here.

6:40 PM
@flawr I suggest using subscripts instead of parentheses for the x(k)
"You can assume that the generated sequence actually contains a fixed point." that's not enough
f(even x) = x
f(odd x) = x + 2
that one has an infinite number of fixed points, but starting from x_1 = 1, you won't find one
oh nevermind
"the generated sequence"
I somehow thought you'd just said "the given function"
your third example doesn't have any fixed points
anyway, another example: f(x) = digit sum of x.

7:34 PM
@MartinEnder oh thanks!
@MartinEnder I've tried, but it looks really ugly, especially for the k+1 expression
@MartinEnder oh cool idea:)

@flawr really? using `<sub>`?

@MartinEnder ah no, using unicode
but <sub> doesn't work in the code environment, doesn't it?

you can always get an HTML code environment with `<code>` (or `<pre><code>` for code blocks)
I prefer bold over code for maths anyway though
example from an answer of Dennis's: codegolf.stackexchange.com/a/104681/8478

I'm trying it right now, but but it seems that `**something**` doesn't make every symbol bold.

hm, okay. well you can always just use `<code>` instead of backticks, then `<sub>` should work.

7:42 PM
@MartinEnder right, that is what I'm changing it to now
@MartinEnder What do you think about the notation `c(x) = x/2 if x is even; 3*x+1 otherwise`

I wonder if there's a neat (i.e. not too contrived) f where every iteration ends in a fixed points, but the fixed points are sparse and have large/unbounded values

as opposed to e.g. `c(x) = if x is even then x/2 otherwise 3*x+1`

@flawr I prefer this one

Thanks for the feedback so far!
@MartinEnder something like `f(x) = x+20*sin(20/abs(x)+1)` might work (after rounding)
but it is difficult to analyze

the Mathematica solution for the challenge is really nice syntactic gibberish... `#//.#2@#&`
although this only works if the fixed point is reached within 2^16 iterations
The alternative is the 10-byte built-in `FixedPoint`

8:31 PM
In haskell it would be `until=<<((==)=<<)` (explanation here)