have a fractal

_posts/2024-11-06-here-have-a-fractal.md

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+---
+title: "Here, Have a Fractal"
+layout: post
+---
+
+# Not feeling it
+
+Today isn't great.
+I don't like it.
+So here, to take minds off things, have a fractal.
+
+![Mandelbrot Set]({{ "/public/mandelbrot.png" | absolute_url }})
+
+Ugly Rust code, using `image` and `num_complex`:
+
+
+```rust
+use image::{ImageBuffer, Rgb};
+use num_complex::Complex;
+
+fn main() {
+    let img = 3200;
+    let scale = 3.0 / img as f32;
+    let max_iter = 42.0;
+    let imgbuf = ImageBuffer::from_par_fn(img, img, |x, y| {
+        let c = Complex::new(x as f32 * scale - 2.25, y as f32 * scale - 1.5);
+        let (mut z, mut i) = (Complex::<f32>::ZERO, 0.0);
+        while i < max_iter && z.norm_sqr() <= 16.0 {
+            z = z * z + c;
+            i += 1.0;
+        }
+        let n = (i as f32) + 1.0 - (0.5 * z.norm().ln()).log2();
+        let h = (n * 360.0 / max_iter + 210.0) % 360.0;
+        let v = (i < max_iter) as u8 as f32;
+        let f = |n: f32| {
+            let k = (n + (h / 60.0)) % 6.0;
+            (255.0 * (v - 0.5 * v * 0f32.max(k.min(4.0 - k).min(1.0)))) as u8
+        };
+        Rgb([f(5.0), f(3.0), f(1.0)])
+    });
+    imgbuf.save("mandelbrot.png").unwrap();
+}
+```