Mandelbrot Fractal Singlethread

main.rs

extern crate num;
use num::Complex;

/// 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`.
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 }
}

#[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` argument 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
                };
        }
    }
}

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

/// Write the buffer `pixels`, whose dimensions are given by `bounds`m to
/// the file named `filename`.
fn write_image(filename: &str, pixels: &[u8], bounds: (usize, usize))
               -> std::io::Result<()> //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(),
                 "Usare: 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");
    // Macro, create a Vector of `0` with dimension `bounds.0 * bounds.1`. 
    let mut pixels = vec![0; bounds.0 * bounds.1];

    render(&mut pixels, bounds, upper_left, lower_right);

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