From 25d1c7c227f694b0b0f31e91b78e9e913f381fc4 Mon Sep 17 00:00:00 2001
From: Jacob <jacob.signorovitch@gmail.com>
Date: Thu, 21 Nov 2024 22:24:24 -0500
Subject: [PATCH] Fractal.

---
 Cargo.lock  | 1012 +++++++++++++++++++++++++++++++++++++++++++++++++++
 Cargo.toml  |    3 +
 src/main.rs |   71 +++-
 3 files changed, 1085 insertions(+), 1 deletion(-)

diff --git a/Cargo.lock b/Cargo.lock
index cd63fc4..cb1ff0a 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -2,6 +2,1018 @@
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diff --git a/Cargo.toml b/Cargo.toml
index e5e1032..b61f0f1 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -4,3 +4,6 @@ version = "0.1.0"
 edition = "2021"
 
 [dependencies]
+image = "0.25.5"
+num-complex = "0.4.6"
+rayon = "1.10.0"
diff --git a/src/main.rs b/src/main.rs
index e7a11a9..74deb21 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,3 +1,72 @@
+use image::{ImageBuffer, Rgb};
+use rayon::prelude::*;
+
+// Image size.
+const IMGW: u32 = 2000;
+const IMGH: u32 = 2000;
+
+// Fractal settings.
+const MAXITER: u32 = 512;
+const ESCRAD: f64 = 2.5;
+
+// Fractal bounds.
+const XMIN: f64 = -2.0;
+const XMAX: f64 = 2.0;
+const YMIN: f64 = -2.0;
+const YMAX: f64 = 2.0;
+
 fn main() {
-    println!("Hello, world!");
+    let w = IMGW as f64;
+    let h = IMGH as f64;
+
+    let pxs: Vec<u8> = (0..IMGH)
+        .into_par_iter()
+        .flat_map(|y| {
+            (0..IMGW)
+                .into_par_iter()
+                .flat_map(move |x| {
+                    let cx = map_range(x as f64, 0.0, w, XMIN, XMAX);
+                    let cy = map_range(y as f64, 0.0, h, YMIN, YMAX);
+                    let c = num_complex::Complex::new(cx, cy);
+
+                    // Compute color for each pixel.
+                    col_map(esc_time(c)).to_vec()
+                })
+                .collect::<Vec<u8>>()
+        })
+        .collect();
+
+    // Create the image from the pixel buffer.
+    let img = ImageBuffer::<Rgb<u8>, _>::from_raw(IMGW, IMGH, pxs).unwrap();
+
+    img.save("h.png").unwrap();
+    println!("Done.");
+}
+
+// Maps a value from one range to another.
+fn map_range(val: f64, imin: f64, imax: f64, omin: f64, omax: f64) -> f64 {
+    omin + (val - imin) * (omax - omin) / (imax - imin)
+}
+
+// Computes the escape time for a given point in the complex plane.
+fn esc_time(c: num_complex::Complex<f64>) -> u32 {
+    let mut z = c;
+    for i in 0..MAXITER {
+        if z.norm() > ESCRAD {
+            return i;
+        }
+        z = (-z).ln() / z.ln();
+    }
+    MAXITER
+}
+
+// Maps the iteration count to a color.
+fn col_map(iter: u32) -> [u8; 3] {
+    if iter == MAXITER {
+        [0, 0, 0] // Black for points that never escape.
+    } else {
+        let t = iter as f64 / MAXITER as f64;
+        let c = (8.5 * (1.0 - t) * (1.0 - t) * (1.0 - t) * t * 255.0) as u8;
+        [c, c, c]
+    }
 }