fractal-poincare/main.rs

use std::env;
use std::fmt::Write;
use std::ops::{Add, Div, Mul, Sub};

#[derive(Debug, Clone, Copy)]
struct Complex {
    re: f64,
    im: f64,
}

impl Complex {
    fn new(re: f64, im: f64) -> Self {
        Complex { re, im }
    }

    fn abs(&self) -> f64 {
        (self.re * self.re + self.im * self.im).sqrt()
    }

    fn powi(&self, mut n: i32) -> Self {
        if n == 0 {
            return Complex::new(1.0, 0.0);
        }
        if n < 0 {
            return Complex::new(1.0, 0.0) / self.powi(-n);
        }

        let mut base = *self;
        let mut result = Complex::new(1.0, 0.0);

        while n > 0 {
            if n % 2 == 1 {
                result = result * base;
            }
            base = base * base;
            n /= 2;
        }
        result
    }
}

// === Complex to Complex ===
impl Add for Complex {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        Complex::new(self.re + rhs.re, self.im + rhs.im)
    }
}

impl Sub for Complex {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self::Output {
        Complex::new(self.re - rhs.re, self.im - rhs.im)
    }
}

impl Mul for Complex {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self::Output {
        Complex::new(
            self.re * rhs.re - self.im * rhs.im,
            self.re * rhs.im + self.im * rhs.re,
        )
    }
}

impl Div for Complex {
    type Output = Self;
    fn div(self, rhs: Self) -> Self::Output {
        let denom = rhs.re * rhs.re + rhs.im * rhs.im;
        Complex::new(
            (self.re * rhs.re + self.im * rhs.im) / denom,
            (self.im * rhs.re - self.re * rhs.im) / denom,
        )
    }
}

// === Complex to f64 ===
impl Add<f64> for Complex {
    type Output = Self;
    fn add(self, rhs: f64) -> Self::Output {
        Complex::new(self.re + rhs, self.im)
    }
}

impl Sub<f64> for Complex {
    type Output = Self;
    fn sub(self, rhs: f64) -> Self::Output {
        Complex::new(self.re - rhs, self.im)
    }
}

impl Mul<f64> for Complex {
    type Output = Self;
    fn mul(self, rhs: f64) -> Self::Output {
        Complex::new(self.re * rhs, self.im * rhs)
    }
}

impl Div<f64> for Complex {
    type Output = Self;
    fn div(self, rhs: f64) -> Self::Output {
        Complex::new(self.re / rhs, self.im / rhs)
    }
}

// === f64 to Complex ===
impl Add<Complex> for f64 {
    type Output = Complex;
    fn add(self, rhs: Complex) -> Complex {
        Complex::new(self + rhs.re, rhs.im)
    }
}

impl Sub<Complex> for f64 {
    type Output = Complex;
    fn sub(self, rhs: Complex) -> Complex {
        Complex::new(self - rhs.re, rhs.im)
    }
}

impl Mul<Complex> for f64 {
    type Output = Complex;
    fn mul(self, rhs: Complex) -> Complex {
        Complex::new(self * rhs.re, self * rhs.im)
    }
}

impl Div<Complex> for f64 {
    type Output = Complex;
    fn div(self, rhs: Complex) -> Complex {
        Complex::new(self, 0.0) / rhs
    }
}

#[derive(Debug)]
struct Args {
    size: u32,
    depth: u8,
    g2: Complex,
    g3: Complex,
}

fn parse_args() -> Args {
    let mut args_struct = Args {
        size: 128,
        depth: 8,
        g2: Complex::new(0.0, 0.0),
        g3: Complex::new(1.0, 0.0),
    };

    let args: Vec<String> = env::args().skip(1).collect();

    let mut i = 0;
    while i < args.len() {
        match args[i].as_str() {
            "--size" | "-s" => {
                if i + 1 < args.len() {
                    args_struct.size = args[i + 1].parse().unwrap_or(args_struct.size);
                    i += 1;
                }
            }
            "--depth" | "-d" => {
                if i + 1 < args.len() {
                    args_struct.depth = args[i + 1].parse().unwrap_or(args_struct.depth);
                    i += 1;
                }
            }
            "-g2" => {
                if i + 1 < args.len() {
                    let val: f64 = args[i + 1].parse().unwrap_or(args_struct.g2.re);
                    args_struct.g2 = Complex::new(val, 0.0);
                    i += 1;
                }
            }
            "-g3" => {
                if i + 1 < args.len() {
                    let val: f64 = args[i + 1].parse().unwrap_or(args_struct.g3.re);
                    args_struct.g3 = Complex::new(val, 0.0);
                    i += 1;
                }
            }
            _ => {}
        }
        i += 1;
    }
    args_struct
}


fn main() {
    let args = parse_args();
    println!("{}", fractal(args.size, args.depth, args.g2, args.g3));
}

fn fractal(size: u32, depth: u8, g2: Complex, g3: Complex) -> String {
    let xi: f64 = -2.0;
    let yi: f64 = -2.0;
    let xf: f64 = 2.0;
    let yf: f64 = 2.0;

    let mut code = String::with_capacity((size * size * 3) as usize);

    for y in 0..=size - 1 {
        let zy = y as f64 * (yf - yi) / (size as f64 - 1.0) + yi;
        for x in 0..=size - 1 {
            let zx = x as f64 * (xf - xi) / (size as f64 - 1.0) + xi;
            let mut z = Complex::new(zx, zy);
            for i in 0..=depth - 1 {
                if z.abs() > 2.0 {
                    write!(&mut code, "{}", i).unwrap();
                    break;
                }
                z = (z.powi(4) + 0.5 * g2 * z.powi(2) + 2.0 * g3 * z + 1.0 / 16.0 * g2.powi(2))
                    / (4.0 * z.powi(3) - g2 * z - g3)
            }
        }
    }
    code
}