mandelbrot.rs

// https://doc.rust-lang.org/std/prelude/index.html

// https://docs.rs/num-complex/0.2.3/num_complex/struct.Complex.html
// https://docs.rs/rayon/1.2.0/rayon/prelude/index.html
use num::Complex;
use rayon::prelude::*;

/// Try to determine if `c` is in the Mandelbrot set, using at most `limit`
/// iterations to decide.
///
/// If `c` is not a member, return `Some(i)`, where `i` is the number of
/// iterations it took for `c` to leave the circle of radius two centered on the
/// origin. If `c` seems to be a member (more precisely, if we reached the
/// iteration limit without being able to prove that `c` is not a member),
/// return `None`.
fn escape_time(c: Complex<f64>, limit: u32) -> Option<u32> {
    let mut z = Complex { re: 0.0, im: 0.0 };
    for i in 0..limit {
        z = z * z + c;
        if z.norm_sqr() > 4.0 {
            return Some(i);
        }
    }

    None
}

use std::str::FromStr;

/// Parse the string `s` as a coordinate pair, like `"400x600"` or `"1.0,0.5"`.
///
/// Specifically, `s` should have the form <left><sep><right>, where <sep> is
/// the character given by the `separator` argument, and <left> and <right> are both
/// strings that can be parsed by `T::from_str`.
///
/// If `s` has the proper form, return `Some<(x, y)>`. If it doesn't parse
/// correctly, return `None`.

// https://doc.rust-lang.org/std/str/trait.FromStr.html
// https://doc.rust-lang.org/core/option/enum.Option.html

fn parse_pair<T: FromStr>(s: &str, separator: char) -> Option<(T, T)> {
    match s.find(separator) {
        None => None,
        Some(index) => {
            match (T::from_str(&s[..index]), T::from_str(&s[index + 1..])) {
                (Ok(l), Ok(r)) => Some((l, r)),
                _ => None
            }
        }
    }
}

#[test]
fn test_parse_pair() {
    assert_eq!(parse_pair::<i32>("",        ','), None);
    assert_eq!(parse_pair::<i32>("10,",     ','), None);
    assert_eq!(parse_pair::<i32>(",10",     ','), None);
    assert_eq!(parse_pair::<i32>("10,20",   ','), Some((10, 20)));
    assert_eq!(parse_pair::<i32>("10,20xy", ','), None);
    assert_eq!(parse_pair::<f64>("0.5x",    'x'), None);
    assert_eq!(parse_pair::<f64>("0.5x1.5", 'x'), Some((0.5, 1.5)));
}

/// Parse a pair of floating-point numbers separated by a comma as a complex
/// number.
fn parse_complex(s: &str) -> Option<Complex<f64>> {
    match parse_pair(s, ',') {
        Some((re, im)) => Some(Complex { re, im }),
        None => None
    }
}

#[test]
fn test_parse_complex() {
    assert_eq!(parse_complex("1.25,-0.0625"),
               Some(Complex { re: 1.25, im: -0.0625 }));
    assert_eq!(parse_complex(",-0.0625"), None);
}

/// Given the row and column of a pixel in the output image, return the
/// corresponding point on the complex plane.
///
/// `bounds` is a pair giving the width and height of the image in pixels.
/// `pixel` is a (column, row) pair indicating a particular pixel in that image.
/// The `upper_left` and `lower_right` parameters are points on the complex
/// plane designating the area our image covers.
fn pixel_to_point(bounds: (usize, usize),
                  pixel: (usize, usize),
                  upper_left: Complex<f64>,
                  lower_right: Complex<f64>)
    -> Complex<f64>
{
    let (width, height) = (lower_right.re - upper_left.re,
                           upper_left.im - lower_right.im);
    Complex {
        re: upper_left.re + pixel.0 as f64 * width  / bounds.0 as f64,
        im: upper_left.im - pixel.1 as f64 * height / bounds.1 as f64
        // Why subtraction here? pixel.1 increases as we go down,
        // but the imaginary component increases as we go up.
    }
}

#[test]
fn test_pixel_to_point() {
    assert_eq!(pixel_to_point((100, 100), (25, 75),
                              Complex { re: -1.0, im:  1.0 },
                              Complex { re:  1.0, im: -1.0 }),
               Complex { re: -0.5, im: -0.5 });
}

/// Render a rectangle of the Mandelbrot set into a buffer of pixels.
///
/// The `bounds` argument gives the width and height of the buffer `pixels`,
/// which holds one grayscale pixel per byte. The `upper_left` and `lower_right`
/// arguments specify points on the complex plane corresponding to the upper-
/// left and lower-right corners of the pixel buffer.
fn render(pixels: &mut [u8],
          bounds: (usize, usize),
          upper_left: Complex<f64>,
          lower_right: Complex<f64>)
{
    assert!(pixels.len() == bounds.0 * bounds.1);

    for row in 0 .. bounds.1 {
        for column in 0 .. bounds.0 {
            let point = pixel_to_point(bounds, (column, row),
                                       upper_left, lower_right);
            pixels[row * bounds.0 + column] =
                match escape_time(point, 255) {
                    None => 0,
                    Some(count) => 255 - count as u8
                };
        }
    }
}

use image::ColorType;
use image::png::PNGEncoder;
use std::fs::File;

/// Write the buffer `pixels`, whose dimensions are given by `bounds`, to the
/// file named `filename`.
fn write_image(filename: &str, pixels: &[u8], bounds: (usize, usize))
    -> Result<(), std::io::Error>
{
    let output = File::create(filename)?;

    let encoder = PNGEncoder::new(output);
    encoder.encode(&pixels,
                   bounds.0 as u32, bounds.1 as u32,
                   ColorType::Gray(8))?;

    Ok(())
}

use std::io::Write;

fn main() {
    let args: Vec<String> = std::env::args().collect();

    if args.len() != 5 {
        writeln!(std::io::stderr(),
                 "Usage: mandelbrot FILE PIXELS UPPERLEFT LOWERRIGHT")
            .unwrap();
        writeln!(std::io::stderr(),
                 "Example: {} mandel.png 1000x750 -1.20,0.35 -1,0.20",
                 args[0])
            .unwrap();
        std::process::exit(1);
    }

    let bounds = parse_pair(&args[2], 'x')
        .expect("error parsing image dimensions");
    let upper_left = parse_complex(&args[3])
        .expect("error parsing upper left corner point");
    let lower_right = parse_complex(&args[4])
        .expect("error parsing lower right corner point");

    let mut pixels = vec![0; bounds.0 * bounds.1];

    // Scope of slicing up `pixels` into horizontal bands.
    {
        let bands: Vec<(usize, &mut [u8])> = pixels
            .chunks_mut(bounds.0)
            .enumerate()
            .collect();

        // https://docs.rs/rayon/1.2.0/rayon/iter/trait.IntoParallelIterator.html#tymethod.into_par_iter
        bands.into_par_iter()
            .weight_max()
            .for_each(|(i, band)| {
                let top = i;
                let band_bounds = (bounds.0, 1);
                let band_upper_left = pixel_to_point(bounds, (0, top),
                                                     upper_left, lower_right);
                let band_lower_right = pixel_to_point(bounds, (bounds.0, top + 1),
                                                      upper_left, lower_right);
                render(band, band_bounds, band_upper_left, band_lower_right);
            });
    }

    write_image(&args[1], &pixels, bounds).expect("error writing PNG file");
}