Add mandlebrot generator example

mandelbrot/Cargo.toml

@@ -0,0 +1,11 @@
+[package]
+name = "mandelbrot"
+version = "0.1.0"
+authors = ["Timothy Warren <twarren@nabancard.com>"]
+edition = "2018"
+
+[dependencies]
+crossbeam = "0.2.8"
+image = "0.13.0"
+num = "0.1.27"
+

mandelbrot/src/main.rs

@@ -0,0 +1,224 @@
+extern crate crossbeam;
+extern crate image;
+extern crate num;
+
+use image::ColorType;
+use image::png::PNGEncoder;
+use num::Complex;
+use std::fs::File;
+use std::io::Write;
+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>("10,20", ','), 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)));
+}
+
+/// 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
+}
+
+/// 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 plan.
+///
+/// `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 pionts on the complex
+/// plain 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 Mandlebrot 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,
+            };
+        }
+    }
+}
+
+/// 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(())
+}
+
+#[allow(dead_code)]
+fn complex_square_add_loop(c: Complex<f64>) {
+    let mut z = Complex { re: 0.0, im: 0.0 };
+    loop {
+        z = z * z + c;
+    }
+}
+
+fn main() {
+    let args: Vec<String> = std::env::args().collect();
+
+    if args.len() != 5 {
+        writeln!(
+            std::io::stderr(),
+            "Usage: mandlebrot FILE PIXELS UPPERLEFT LOWERRIGHT"
+        ).unwrap();
+
+        writeln!(
+            std::io::stderr(),
+            "Example: {} mandle.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];
+
+    // render(&mut pixels, bounds, upper_left, lower_right);
+
+    let threads = 8;
+    let rows_per_band = bounds.1 / threads + 1;
+
+    {
+        let bands: Vec<&mut [u8]> = pixels
+            .chunks_mut(rows_per_band * bounds.0)
+            .collect();
+        crossbeam::scope(|spawner| {
+            for (i, band) in bands.into_iter().enumerate() {
+                let top = rows_per_band * i;
+                let height = band.len() / bounds.0;
+                let band_bounds = (bounds.0, height);
+                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 + height), upper_left, lower_right);
+
+                spawner.spawn(move || {
+                    render(band, band_bounds, band_upper_left, band_lower_right);
+                });
+            }
+        });
+    }
+
+    write_image(&args[1], &pixels, bounds)
+        .expect("error writing PNG file");
+}