add example drawing a dragon curve (#29)

* add example drawing a dragon curve

* add comments describing the dragon curve example

examples/dragon.rs

@@ -0,0 +1,90 @@
+//! Draw a dragon curve, more specifically a highway dragon.
+//! (https://en.wikipedia.org/wiki/Dragon_curve)
+//!
+//! As can be seen in the above wikipedia article, the highway dragon can be
+//! constructed by repeatedly folding a strip of paper and looking at the
+//! directions of the folds/turns.
+//!
+//! Starting with a strip going left to right (l2r):
+//!
+//! start|--->---l2r--->---|end
+//!
+//! you might fold it like this:
+//!
+//! end|---<---r2l---<---\
+//! start|->---l2r--->---/
+//!
+//! Getting a l2r strip, followed by a left turn, followed by a r2l strip.
+//!
+//! Folding a right to left strip:
+//!
+//! end|---<---r2l---<---|start
+//!
+//! In the same way:
+//!
+//! start|-->---l2r--->---\
+//! end|----<---r2l---<---/
+//!
+//! Would give you a l2r, followed by a right turn, followed by a r2l strip.
+//!
+//! As you can see, the only difference between the two is the direction of
+//! the turn in the middle.
+//!
+//! This folding of paper is simulated by recursively calling the dragon(..)
+//! function, passing the direction of the turn for this fold as an angle
+//! (+90 for a right turn, -90 for a left turn).
+
+extern crate turtle;
+
+use turtle::Turtle;
+use turtle::Color;
+
+fn main() {
+    let mut turtle = Turtle::new();
+
+    turtle.set_background_color("#112244");
+
+    turtle.pen_up();
+    turtle.backward(160.0);
+    turtle.right(90.);
+    turtle.forward(110.);
+    turtle.pen_down();
+    turtle.set_speed(10);
+
+    dragon(&mut turtle, -90., 11, 0., 255.);
+
+    turtle.hide();
+}
+
+/// Draw the dragon curve by simulating folding a strip of paper
+///
+/// `fold_direction`: The direction of the fold, +90 for a right, -90 for a
+/// left turn.
+/// `num_folds`: The number of times to fold the 'strip of paper'.
+/// `color_start`/`color_end`: The color at the start/end of this subsection
+/// of the curve as a number 0-255.
+fn dragon(
+    turtle: &mut Turtle,
+    fold_direction: f64,
+    num_folds: usize,
+    color_start: f64,
+    color_end: f64,
+) {
+    let color_mid = (color_start + color_end) * 0.5;
+    if num_folds == 0 {
+        // mapping a color number 0-255 to an rgb gradient.
+        turtle.set_pen_color(Color {
+            red: (color_mid - 128.).abs() * 2.,
+            green: color_mid,
+            blue: 160.,
+            alpha: 1.,
+        });
+        return turtle.forward(10.);
+    }
+
+    // draw a left to right strip (which has a left turn in the middle)
+    dragon(turtle, -90., num_folds - 1, color_start, color_mid);
+    turtle.right(fold_direction);
+    // draw a right to left strip (which has a right turn in the middle)
+    dragon(turtle, 90., num_folds - 1, color_mid, color_end);
+}