Mandelbrot

Cargo.lock

@@ -2,6 +2,12 @@
 # It is not intended for manual editing.
 version = 3
 
+[[package]]
+name = "autocfg"
+version = "1.4.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ace50bade8e6234aa140d9a2f552bbee1db4d353f69b8217bc503490fc1a9f26"
+
 [[package]]
 name = "bitflags"
 version = "1.3.2"
@@ -24,6 +30,7 @@ checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd"
 name = "fractals"
 version = "0.1.0"
 dependencies = [
+ "num",
  "sdl2",
 ]
 
@@ -39,6 +46,79 @@ version = "0.2.159"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "561d97a539a36e26a9a5fad1ea11a3039a67714694aaa379433e580854bc3dc5"
 
+[[package]]
+name = "num"
+version = "0.4.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "35bd024e8b2ff75562e5f34e7f4905839deb4b22955ef5e73d2fea1b9813cb23"
+dependencies = [
+ "num-bigint",
+ "num-complex",
+ "num-integer",
+ "num-iter",
+ "num-rational",
+ "num-traits",
+]
+
+[[package]]
+name = "num-bigint"
+version = "0.4.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a5e44f723f1133c9deac646763579fdb3ac745e418f2a7af9cd0c431da1f20b9"
+dependencies = [
+ "num-integer",
+ "num-traits",
+]
+
+[[package]]
+name = "num-complex"
+version = "0.4.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "73f88a1307638156682bada9d7604135552957b7818057dcef22705b4d509495"
+dependencies = [
+ "num-traits",
+]
+
+[[package]]
+name = "num-integer"
+version = "0.1.46"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7969661fd2958a5cb096e56c8e1ad0444ac2bbcd0061bd28660485a44879858f"
+dependencies = [
+ "num-traits",
+]
+
+[[package]]
+name = "num-iter"
+version = "0.1.45"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1429034a0490724d0075ebb2bc9e875d6503c3cf69e235a8941aa757d83ef5bf"
+dependencies = [
+ "autocfg",
+ "num-integer",
+ "num-traits",
+]
+
+[[package]]
+name = "num-rational"
+version = "0.4.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f83d14da390562dca69fc84082e73e548e1ad308d24accdedd2720017cb37824"
+dependencies = [
+ "num-bigint",
+ "num-integer",
+ "num-traits",
+]
+
+[[package]]
+name = "num-traits"
+version = "0.2.19"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "071dfc062690e90b734c0b2273ce72ad0ffa95f0c74596bc250dcfd960262841"
+dependencies = [
+ "autocfg",
+]
+
 [[package]]
 name = "sdl2"
 version = "0.37.0"

Cargo.toml

@@ -6,4 +6,5 @@ edition = "2021"
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
+num = "0.4.3"
 sdl2 = { version = "0.37", features = ["gfx"] }

README.md

@@ -0,0 +1,4 @@
+## rust-sdl2-fractals
+
+[![mandelbrot](./examples/mandelbrot.png?raw=true)](https://en.wikipedia.org/wiki/Mandelbrot_set)
+[![snowflake](./examples/snowflake.png?raw=true)](https://en.wikipedia.org/wiki/Koch_snowflake)

src/koch_snowflake.rs

@@ -0,0 +1,133 @@
+extern crate sdl2;
+
+use std::cmp::min;
+
+use sdl2::event::Event;
+use sdl2::keyboard::Keycode;
+use sdl2::pixels::{self, Color};
+
+use sdl2::gfx::primitives::DrawRenderer;
+use sdl2::render::WindowCanvas;
+
+const SCREEN_WIDTH: i16 = 800;  // i15
+const SCREEN_HEIGHT: i16 = 600;  // i15
+
+fn atan(a: f32, b: f32) -> f32 {
+    if b == 0.0 {
+        return 0.0
+    } else if b < 0.0 {
+        return (a/b).atan() + std::f32::consts::PI;
+    } else {
+        return (a/b).atan();
+    }
+}
+
+/** for each zoomlevel, lines are replaced by 4 new lines of length a/3 **/
+fn koch_line(canvas: &WindowCanvas, x0: i16, y0: i16, x4: i16, y4: i16, color: Color, zoom: i16) {
+
+  if zoom == 1 {
+      let _ = canvas.line(x0, y0, x4, y4, color);
+  } else {
+      /* the outer two lines */
+      let x1 = x0 + (x4-x0) / 3;
+      let y1 = y0 + (y4-y0) / 3;
+      let x3 = x0 + 2* (x4-x0) / 3;
+      let y3 = y0 + 2* (y4-y0) / 3;
+      koch_line(canvas, x0, y0, x1, y1, color, zoom-1);
+      koch_line(canvas, x3, y3, x4, y4, color, zoom-1);
+
+      /* the inner two lines (arms of an equilateral triangle) */
+      let dx = x3 - x1;
+      let dy = y3 - y1;
+      let a = ((dx*dx + dy*dy) as f32).sqrt();
+      let angle = atan((-dy).into(), dx.into());  // angle of the original line 
+      const INTERNAL_ANGLE: f32 = std::f32::consts::FRAC_PI_3;  // 60_f32.to_radians();
+      let x2 = x1 + ((a * (angle - INTERNAL_ANGLE).cos()) as i16);
+      let y2 = y1 - ((a * (angle - INTERNAL_ANGLE).sin()) as i16);
+      koch_line(canvas, x1, y1, x2, y2, color, zoom-1);
+      koch_line(canvas, x2, y2, x3, y3, color, zoom-1);
+  }
+}
+
+fn koch_snowflake(canvas: &WindowCanvas, x: i16, y: i16, a: i16, color: Option<Color>, zoom: i16) {
+    let max_zoom = (a as f32).log(3.0).ceil() as i16;
+    let effective_zoom = min(zoom, max_zoom);
+    println!("zoom: {}/{}", effective_zoom, max_zoom);
+
+    let c = (255 * (effective_zoom-1) / (max_zoom-1)) as u8;
+    let color = color.unwrap_or(Color::RGB(c, c, 127+c/2));
+
+    let h = (a as f32 * 3.0_f32.sqrt() / 2.0) as i16;  // height of equilateral triangle
+
+    let x1 = x;
+    let y1 = y - h/2;
+    let x2 = x - a/2;
+    let y2 = y + h/2;
+    let x3 = x + a/2;
+    let y3 = y + h/2;
+    koch_line(&canvas, x1, y1, x2, y2, color, effective_zoom);
+    koch_line(&canvas, x2, y2, x3, y3, color, effective_zoom);
+    koch_line(&canvas, x3, y3, x1, y1, color, effective_zoom);
+}
+
+fn main() -> Result<(), String> {
+    let sdl_context = sdl2::init()?;
+    let video_subsys = sdl_context.video()?;
+    let window = video_subsys
+        .window(
+            "rust-sdl2_gfx: draw line & FPSManager",
+            (SCREEN_WIDTH as u16).into(),
+            (SCREEN_HEIGHT as u16).into(),
+        )
+        .position_centered()
+        .opengl()
+        .build()
+        .map_err(|e| e.to_string())?;
+
+    let mut canvas = window.into_canvas().build().map_err(|e| e.to_string())?;
+
+    canvas.set_draw_color(pixels::Color::RGB(0, 0, 0));
+    canvas.clear();
+    canvas.present();
+    println!("Welcome :)");
+    println!("[Klick] into canvas to draw a koch snowflake…");
+    println!("Press [Space] to clear the canvas…");
+    println!("Press [Backspace] to reset the zoom…");
+
+    let mut events = sdl_context.event_pump()?;
+
+    let mut zoom = 1;
+
+    'main: loop {
+        for event in events.poll_iter() {
+            match event {
+                Event::Quit { .. } => break 'main,
+
+                Event::KeyDown {
+                    keycode: Some(keycode),
+                    ..
+                } => {
+                    if keycode == Keycode::Escape {
+                        break 'main;
+                    } else if keycode == Keycode::Space {
+                        canvas.set_draw_color(pixels::Color::RGB(0, 0, 0));
+                        canvas.clear();
+                        canvas.present();
+                    } else if keycode == Keycode::BACKSPACE {
+                        zoom = 1
+                    }
+                }
+
+                Event::MouseButtonDown { x, y, .. } => {
+                    koch_snowflake(&canvas, x.try_into().unwrap(), y.try_into().unwrap(), SCREEN_HEIGHT/3, None, zoom);
+                    canvas.present();
+                    zoom += 1;
+                }
+
+                _ => {}
+            }
+        }
+    }
+
+    Ok(())
+}

src/main.rs

@@ -1,6 +1,9 @@
 extern crate sdl2;
 
-use std::cmp::min;
+use core::f32;
+use std::i32;
+
+use num::complex::{Complex, Complex32, ComplexFloat};
 
 use sdl2::event::Event;
 use sdl2::keyboard::Keycode;
@@ -9,65 +12,120 @@ use sdl2::pixels::{self, Color};
 use sdl2::gfx::primitives::DrawRenderer;
 use sdl2::render::WindowCanvas;
 
-const SCREEN_WIDTH: i16 = 800;  // i15
+fn bound(n: f32, min: f32, max: f32) -> f32 {
-const SCREEN_HEIGHT: i16 = 600;  // i15
+    let mut vals = [min, n, max];
+    vals.sort_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal));
+    vals[1]
+}
 
-fn atan(a: f32, b: f32) -> f32 {
+fn norm(n: f32, min: f32, max: f32) -> f32 {
-    if b == 0.0 {
+    let n_bound = bound(n, min, max);
-        return 0.0
+    (n_bound-min) / (max-min)
-    } else if b < 0.0 {
+}
-        return (a/b).atan() + std::f32::consts::PI;
+
-    } else {
+fn norm_u8(n: f32, min: f32, max: f32) -> u8 {
-        return (a/b).atan();
+    (255.0 * norm(n, min, max)) as u8
+}
+
+const SCREEN_WIDTH: i16 = 800;
+const SCREEN_HEIGHT: i16 = 600;
+const WIDTH: usize = SCREEN_WIDTH as usize;
+const HEIGHT: usize = SCREEN_HEIGHT as usize;
+
+fn xy2complex(x: f32, y: f32) -> Complex32 {
+    let x_min = -2.0;
+    let x_max = 1.0;
+    let y_min = -2.0;
+    let y_max = 2.0;
+
+    Complex::new(x_min + (x_max-x_min) * x / WIDTH as f32,
+                 -(y_min + (y_max-y_min) * y / HEIGHT as f32))
+}
+
+pub struct Mandelbrot {
+    pub divergence: Vec<Vec<i32>>,  // iteration when diverged (if not diverged: i32::MAX)
+    pub projections: Vec<Vec<Complex<f32>>>,
+    pub cs: Vec<Vec<Complex32>>,
+    pub iteration: i32,
+}
+
+impl Mandelbrot {
+    fn new() -> Mandelbrot {
+        let divergence = vec![vec![i32::MAX; WIDTH]; HEIGHT];
+        let projections = vec![vec![Complex::new(0.0,0.0); WIDTH]; HEIGHT];
+        let mut cs = vec![vec![Complex::new(0.0,0.0); WIDTH]; HEIGHT];
+
+        for y in 0..cs.len() {
+            for x in 0..cs[y].len() {
+                cs[y][x] = xy2complex((x as i16).into(), (y as i16).into());
             }
         }
 
-/** for each zoomlevel, lines are replaced by 4 new lines of length a/3 **/
+        let iteration = 0;
-fn koch_line(canvas: &WindowCanvas, x0: i16, y0: i16, x4: i16, y4: i16, color: Color, zoom: i16) {
 
-  if zoom == 1 {
+        Mandelbrot {
-      let _ = canvas.line(x0, y0, x4, y4, color);
+            divergence,
-  } else {
+            projections,
-      /* the outer two lines */
+            cs,
-      let x1 = x0 + (x4-x0) / 3;
+            iteration,
-      let y1 = y0 + (y4-y0) / 3;
-      let x3 = x0 + 2* (x4-x0) / 3;
-      let y3 = y0 + 2* (y4-y0) / 3;
-      koch_line(canvas, x0, y0, x1, y1, color, zoom-1);
-      koch_line(canvas, x3, y3, x4, y4, color, zoom-1);
-
-      /* the inner two lines (arms of an equilateral triangle) */
-      let dx = x3 - x1;
-      let dy = y3 - y1;
-      let a = ((dx*dx + dy*dy) as f32).sqrt();
-      let angle = atan((-dy).into(), dx.into());  // angle of the original line 
-      const INTERNAL_ANGLE: f32 = std::f32::consts::FRAC_PI_3;  // 60_f32.to_radians();
-      let x2 = x1 + ((a * (angle - INTERNAL_ANGLE).cos()) as i16);
-      let y2 = y1 - ((a * (angle - INTERNAL_ANGLE).sin()) as i16);
-      koch_line(canvas, x1, y1, x2, y2, color, zoom-1);
-      koch_line(canvas, x2, y2, x3, y3, color, zoom-1);
         }
     }
 
-fn koch_snowflake(canvas: &WindowCanvas, x: i16, y: i16, a: i16, color: Option<Color>, zoom: i16) {
+    fn iter(&mut self) {
-    let max_zoom = (a as f32).log(3.0).ceil() as i16;
+        self.iteration += 1;
-    let effective_zoom = min(zoom, max_zoom);
+        println!("iteration={}", self.iteration);
-    println!("zoom: {}/{}", effective_zoom, max_zoom);
 
-    let c = (255 * (effective_zoom-1) / (max_zoom-1)) as u8;
+        let projections = &mut self.projections;
-    let color = color.unwrap_or(Color::RGB(c, c, 127+c/2));
+        let divergence = &mut self.divergence;
+        for y in 0..projections.len() {
+            for x in 0..projections[y].len() {
+                if divergence[y][x] > self.iteration {
+                    projections[y][x] = projections[y][x] * projections[y][x] + self.cs[y][x];
 
-    let h = (a as f32 * 3.0_f32.sqrt() / 2.0) as i16;  // height of equilateral triangle
+                    if projections[y][x].abs().is_nan() {  // or greater bounds
+                        divergence[y][x] = self.iteration;
+                    }
+                }
+            }
+        }
+    }
+
+    fn show_divergence<'a>(&self, canvas: &'a mut WindowCanvas) {
+        let values = &self.divergence;
+        for y in 0..values.len() {
+            for x in 0..values[y].len() {
+                let v = values[y][x];
+                let r = norm_u8(0.0 - v.abs_diff(20) as f32, -10.0, 10.0);
+                let g = norm_u8(0.0 - v.abs_diff(30) as f32, -10.0, 10.0);
+                let b = norm_u8(v as f32, 0.0, 50.0);
+                let color = Color::RGB(r, g, b);
+                let _ = canvas.box_(x as i16, y as i16, x as i16, y as i16, color);
+            }
+        }
+        canvas.present();
+    }
+
+    fn show_projections<'a>(&self, canvas: &'a mut WindowCanvas) {
+        let values = &self.projections;
+        for y in 0..values.len() {
+            for x in 0..values[y].len() {
+                let v = values[y][x];
+                let im = norm_u8(v.im, -2.0, 2.0);
+                let re = norm_u8(v.re, -2.0, 2.0);
+                let color = Color::RGB(0, re, im);
+                let _ = canvas.box_(x as i16, y as i16, x as i16, y as i16, color);
+            }
+        }
+        canvas.present();
+    }
+
+    fn debug(&self, x: usize, y: usize) {
+        println!("");
+        println!("y={}, x={}, c={}", y, x, self.cs[y][x]);  // xy2complex((x as i16).into(), (y as i16).into())
+        println!("projection={}, abs={}", self.projections[y][x], self.projections[y][x].abs());
+        println!("divergence={}", self.divergence[y][x]);
+    }
 
-    let x1 = x;
-    let y1 = y - h/2;
-    let x2 = x - a/2;
-    let y2 = y + h/2;
-    let x3 = x + a/2;
-    let y3 = y + h/2;
-    koch_line(&canvas, x1, y1, x2, y2, color, effective_zoom);
-    koch_line(&canvas, x2, y2, x3, y3, color, effective_zoom);
-    koch_line(&canvas, x3, y3, x1, y1, color, effective_zoom);
 }
 
 fn main() -> Result<(), String> {
@@ -75,7 +133,7 @@ fn main() -> Result<(), String> {
     let video_subsys = sdl_context.video()?;
     let window = video_subsys
         .window(
-            "rust-sdl2_gfx: draw line & FPSManager",
+            "rust-sdl2-fractals",
             (SCREEN_WIDTH as u16).into(),
             (SCREEN_HEIGHT as u16).into(),
         )
@@ -89,16 +147,20 @@ fn main() -> Result<(), String> {
     canvas.set_draw_color(pixels::Color::RGB(0, 0, 0));
     canvas.clear();
     canvas.present();
-    println!("Welcome :)");
+
-    println!("[Klick] into canvas to draw a koch snowflake…");
+    let mut mandelbrot = Mandelbrot::new();
-    println!("Press [Space] to clear the canvas…");
-    println!("Press [Backspace] to reset the zoom…");
 
     let mut events = sdl_context.event_pump()?;
 
-    let mut zoom = 1;
+    println!("Press [Space] to show next iteration (projections)…");
+    println!("Press [Enter] to show next iteration (divergence)…");
+    println!("[Klick] any coordinate for debug output…");
+    
+    mandelbrot.iter();
+    mandelbrot.show_projections(&mut canvas);
 
     'main: loop {
+
         for event in events.poll_iter() {
             match event {
                 Event::Quit { .. } => break 'main,
@@ -109,21 +171,20 @@ fn main() -> Result<(), String> {
                 } => {
                     if keycode == Keycode::Escape {
                         break 'main;
-                    } else if keycode == Keycode::Space {
+                    } else if keycode == Keycode::SPACE {
-                        canvas.set_draw_color(pixels::Color::RGB(0, 0, 0));
+                        mandelbrot.iter();
-                        canvas.clear();
+                        mandelbrot.show_projections(&mut canvas);
-                        canvas.present();
+                    } else if keycode == Keycode::RETURN {
+                        mandelbrot.show_divergence(&mut canvas);
+                        mandelbrot.iter();
                     } else if keycode == Keycode::BACKSPACE {
-                        zoom = 1
+                        mandelbrot.show_projections(&mut canvas);
                     }
                 }
 
                 Event::MouseButtonDown { x, y, .. } => {
-                    koch_snowflake(&canvas, x.try_into().unwrap(), y.try_into().unwrap(), SCREEN_HEIGHT/3, None, zoom);
+                    mandelbrot.debug(x.try_into().unwrap(), y.try_into().unwrap());
-                    canvas.present();
-                    zoom += 1;
                 }
-
                 _ => {}
             }
         }