neither an understatement nor an overstatement, a Big-Theta

Automata and formal languages were pretty much my entire "Theory of Computation" class. It's what's in Sipser.

Didn’t you go into Turing machines and the Halting problem from that?

That was my intro into computation: regex, automatas, state machines, stack state machines, formal languages, grammars, Turing machines, Hanting Problem, P NP.

sigma star.

if you haven't heard about theory of computation, let me define some keywords:

• symbol: smallest unit. denoted by any character(a,b,c, etc.) or number (0,1, etc.)
• alphabet: set of symbols. denoted by Σ(sigma). e.g.: {a, b, c}
• string: sequence of symbols. eg: a, aa, aaab, etc.
• language: set of strings. e.g.: {a, as, aaab, ...}

now, sigma has powers. Σ² is set of all strings of length 2. e.g.: {aa, ab, bb, ...}. you can generalise this to Σ^n.
Σ* is union of all powers of sigma. i.e., Σ¹ + Σ² + ...

so, a language is basically a subset of Σ*.

as for why theory of computation even exists, you basically try to define what a computer can/cannot do.
and you try to mathematically define a computer. then you try to define what a language is(in case of programming , you need it to form languages and compilers). hence the need for this.

A tree can be seen as a formal language. Look into L-systems.

If you generalize what a symbol is (the rgb value of a pixel) you can write a grammar that ends producing a list of pixels. You can then place it in a 2d matrix and you have an image.

I guess a better approach would be wave function colapse, but seems to me like it could be formally described as a grammar (CS or CF, dunno, would have to look into it)

what'd a symbol be? a pixel?

aside from this, they say a picture is worth a 1000 words. so maybe a big language.

They don't have anything to do with alphabets in theory of computation...

thanks for sharing. can't wait to go insane :')