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()
}

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  

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  

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

I was sad to discover that division wasn’t actual complex division. As in some other languages, one has to implement this “division” by hand because the library designers assume that you never want truncating integer division together with complex numbers. Which is reasonable, I guess.

(ql:quickload :cl-ppcre)
(ql:quickload :str)

(defun parse-line (line)
  (ppcre:register-groups-bind
      (name x y)
      ("^([A-Za-z]+)=[[]([\-0-9.]+),([\-0-9.]+)[]]$" line)
    (cons name (complex (parse-integer x) (parse-integer y)))))

(defun read-inputs (filename)
  (let ((input-lines (uiop:read-file-lines filename)))
    (parse-line (car input-lines))))

(defun fake-complex-division (y d)
  (complex (truncate (realpart y) (realpart d))
           (truncate (imagpart y) (imagpart d))))

(defun f (x a)
  (+ a (fake-complex-division (* x x) #C(10 10))))

(defun main-1 (filename)
  (let* ((a (cdr (read-inputs filename)))
         (result (f (f (f #C(0 0) a) a) a)))
    (str:concat "["
                (write-to-string (realpart result))
                ","
                (write-to-string (imagpart result))
                "]")))

(defun engrave? (p)
  (labels ((iter (x n)
             (if (zerop n)
                 t
                 (let ((next-x (+ p (fake-complex-division (* x x) #C(100000 100000)))))
                   (if (or (> (abs (realpart next-x)) 1000000)
                           (> (abs (imagpart next-x)) 1000000))
                       nil
                       (iter next-x (- n 1)))))))
    (iter 0 100)))

(defun count-engraves (a spacing)
  (let ((steps (/ 1000 spacing)))
    (loop for x from 0 to steps
          sum (loop for y from 0 to steps
                    for p = (+ a (complex (* spacing x) (* spacing y)))
                    sum (if (engrave? p) 1 0)))))

(defun main-2 (filename)
  (count-engraves (cdr (read-inputs filename)) 10))

(defun main-3 (filename)
  (count-engraves (cdr (read-inputs filename)) 1))