For quest 2, I decided to implement my own Complex type and operators, because I expected parts 2 and 3 to have something unconventional, but alas it’s just a regular Mandelbrot fractal.

Nim again, Nim forever:

type Complex = tuple[x,y: int]
proc `$`(c: Complex): string = &"[{c.x},{c.y}]"
proc `+`(a,b: Complex): Complex = (a.x+b.x, a.y+b.y)
proc `-`(a,b: Complex): Complex = (a.x-b.x, a.y-b.y)
proc `*`(a,b: Complex): Complex = (a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x)
proc `/`(a,b: Complex): Complex = (a.x div b.x, a.y div b.y)
proc `/`(a: Complex, b: int): Complex = (a.x div b, a.y div b)

proc parseInput(input: string): Complex =
  let parts = input.split({'=','[',',',']'})
  (parseInt(parts[2]), parseInt(parts[3]))

proc isStable(point: Complex, iter: int): bool =
  var num: Complex
  for _ in 1..iter:
    num = (num * num) / 100_000 + point
    if num.x notin -1_000_000 .. 1_000_000 or
       num.y notin -1_000_000 .. 1_000_000:
      return false
  true

proc solve_part1*(input: string): Solution =
  let start = parseInput(input)
  var point: Complex
  for _ in 1..3:
    point = (point * point) / 10 + start
  result := $point

proc solve_part2*(input: string): Solution =
  let start = parseInput(input)
  for y in 0..100:
    for x in 0..100:
      let point: Complex = (start.x + 10 * x, start.y + 10 * y)
      if point.isStable(iter=100): inc result.intVal

proc solve_part3*(input: string): Solution =
  let start = parseInput(input)
  for y in 0..1000:
    for x in 0..1000:
      let point: Complex = (start.x + x, start.y + y)
      if point.isStable(iter=100): inc result.intVal

Full solution at Codeberg: solution.nim

FSharp
(my first submission failed, so I may not be as detailed here)

I laugh at how long this took me. At first I got stuck due to checked arithmetic. In FSharp you open the Checked module and you get the overloaded operators for primitives, whereas CSharp is checked {a + b}. I also mistakenly used distinct on part 3 when I didn’t need it.

I did appreciate the choose functions of functional programming, which returns all of the Some values of a sequence of options. The PSeq library let me use 70% of the cpu on the calculations :)

module EveryBodyCodes2025.Quest02  

open System.IO  
open System.Text.RegularExpressions  
open FSharp.Collections.ParallelSeq  
open Checked  

[<Struct>]  
type ComplexNumber = 
    {X: int64; Y: int64}  
    static member (+) (a: ComplexNumber, b: ComplexNumber) = {X = a.X + b.X; Y = a.Y + b.Y }  
    static member (*) (a: ComplexNumber, b: ComplexNumber) = { X = ( a.X * b.X ) - (a.Y * b.Y); Y = (a.X * b.Y) + (a.Y * b.X) }  
    static member (/) (a: ComplexNumber, b: ComplexNumber) = { X = a.X / b.X; Y = a.Y / b.Y }  
    override this.ToString() = $"[{this.X},{this.Y}]"  
    
let parseInput file =  
    File.ReadAllLines file  
    |> fun lines ->  
        let reg = Regex(@"A=\[(-?\d+),(-?\d+)\]")  
        let res = reg.Match(lines[0])  
        match res.Success with  
        | true ->  
            let x = int64 res.Groups[1].Value  
            let y = int64 res.Groups[2].Value  
            {X = x; Y = y}  
        | false -> failwith "failed to parse"  
        
    
let part1 () =  
    parseInput "Inputs/Quest02/Q02_P01.txt"  
    |> fun a ->  
        [1..3]  
        |> List.fold (fun acc _ -> (acc * acc) / { X = 10; Y = 10 } + a ) {X = 0; Y = 0}  

let cycle p =  
    let rec iterate current iteration =  
        if iteration = 100 then Some current  
        else  
            let next = (current * current) / {X = 100_000; Y = 100_000 } + p  
            if abs(next.X) > 1_000_000 || abs(next.Y) > 1_000_000 then  
                None  
            else iterate next (iteration + 1)  
    iterate { X = 0; Y = 0 } 0  

let part2 () =  
    parseInput "Inputs/Quest02/Q02_P02.txt"  
    |> fun a ->  
        seq {  
            for y in 0..100 do  
            for x in 0..100 do  
                yield {X = a.X + (int64 x * 10L); Y = a.Y + (int64 y * 10L)}  
        }  
        |> PSeq.choose cycle  
        |> PSeq.distinct  
        |> PSeq.length  

let part3 () =  
    parseInput "Inputs/Quest02/Q02_P03.txt"  
    |> fun a ->  
        seq {  
            for y in 0..1000 do  
            for x in 0..1000 do  
                yield {X = a.X + (int64 x); Y = a.Y + (int64 y)}  
        }  
        |> PSeq.choose cycle  
        |> PSeq.length  

It’s gradually coming back to me. The Haskell Complex type doesn’t work particularly nicely as an integer, plus the definition of division is more like “scale”, so I just went with my own type.

Then I forgot which of div and quot I should use, and kept getting nearly the right answer :/

import Data.Ix  

data CNum = CNum !Integer !Integer  

instance Show CNum where  
  show (CNum x y) = "[" ++ show x ++ "," ++ show y ++ "]"  

cadd, cmul, cdiv :: CNum -> CNum -> CNum  
(CNum x1 y1) `cadd` (CNum x2 y2) = CNum (x1 + x2) (y1 + y2)  
(CNum x1 y1) `cmul` (CNum x2 y2) = CNum (x1 * x2 - y1 * y2) (x1 * y2 + y1 * x2)  
(CNum x1 y1) `cdiv` (CNum x2 y2) = CNum (x1 `quot` x2) (y1 `quot` y2)  

part1 a = iterate op (CNum 0 0) !! 3  
  where  
    op x = ((x `cmul` x) `cdiv` CNum 10 10) `cadd` a  

countEngraved = length . filter engrave  
  where  
    engrave p =  
      let rs = take 100 $ tail $ iterate (op p) (CNum 0 0)  
       in all (\(CNum x y) -> abs x <= 1000000 && abs y <= 1000000) rs  
    op p r = ((r `cmul` r) `cdiv` CNum 100000 100000) `cadd` p  

part2 a =  
  countEngraved  
    . map (\(y, x) -> a `cadd` CNum (x * 10) (y * 10))  
    $ range ((0, 0), (100, 100))  

part3 a =  
  countEngraved  
    . map (\(y, x) -> a `cadd` CNum x y)  
    $ range ((0, 0), (1000, 1000))  

main = do  
  print $ part1 $ CNum 164 56  
  print $ part2 $ CNum (-21723) 67997  
  print $ part3 $ CNum (-21723) 67997  

Rust

use log::debug;
use std::collections::HashSet;

use regex::Regex;

#[derive(PartialEq, Eq, Hash, Clone)]
struct Number(isize, isize);

impl Number {

  fn add(self: &Number, b: &Number) -> Number {
    Number(self.0 + b.0, self.1 + b.1)
  }

  fn mul(self: &Number, b: &Number) -> Number {
    Number(self.0 * b.0 - self.1 * b.1, self.0 * b.1 + self.1 * b.0)
  }

  fn div(self: &Number, b: &Number) -> Number {
    Number(self.0 / b.0, self.1 / b.1)
  }
}

pub fn solve_part_1(input: &str) -> String {
  let re = Regex::new(r"A=\[(\d+),(\d+)\]").unwrap();
  let (_, [x, y]) = re.captures(input).unwrap().extract();
  let a = Number(x.parse().unwrap(), y.parse().unwrap());
  let mut res = Number(0, 0);
  for _ in 0..3 {
    res = res.mul(&res);
    res = res.div(&Number(10, 10));
    res = res.add(&a);
  }
  format!("[{},{}]", res.0, res.1)
}

pub fn solve_part_2(input: &str) -> String {
  let re = Regex::new(r"A=\[([-0-9]+),([-0-9]+)\]").unwrap();
  let (_, [x, y]) = re.captures(input).unwrap().extract();
  let a = Number(x.parse().unwrap(), y.parse().unwrap());
  let mut engraved_points = 0;
  let mut pts: HashSet<_> = HashSet::new();
  for i in 0..=100 {
    for j in 0..=100 {
      let pt = Number(a.0 + 10 * i, a.1 + 10 * j);
      let mut res = Number(0, 0);
      engraved_points += 1;
      pts.insert(pt.clone());
      for _ in 0..100 {
        res = res.mul(&res);
        res = res.div(&Number(100_000, 100_000));
        res = res.add(&pt);
        if res.0.abs() > 1_000_000 || res.1.abs() > 1_000_000 {
          engraved_points -= 1;
          pts.remove(&pt);
          break;
        }
      }
    }
  }
  for i in 0..=100 {
    debug!("{}", (0..=100).map(|j| if pts.contains(&Number(a.0 + 10*i, a.1 + 10*j)) { 'X' } else {'.'}).collect::<String>());
  }
  engraved_points.to_string()
}

pub fn solve_part_3(input: &str) -> String {
  let re = Regex::new(r"A=\[([-0-9]+),([-0-9]+)\]").unwrap();
  let (_, [x, y]) = re.captures(input).unwrap().extract();
  let a = Number(x.parse().unwrap(), y.parse().unwrap());
  let mut engraved_points = 0;
  for i in 0..=1000 {
    for j in 0..=1000 {
      let pt = Number(a.0 + i, a.1 + j);
      let mut res = Number(0, 0);
      engraved_points += 1;
      for _ in 0..100 {
        res = res.mul(&res);
        res = res.div(&Number(100_000, 100_000));
        res = res.add(&pt);
        if res.0.abs() > 1_000_000 || res.1.abs() > 1_000_000 {
          engraved_points -= 1;
          break;
        }
      }
    }
  }
  engraved_points.to_string()
}