diff --git a/CLAUDE.md b/CLAUDE.md
index b68a294..204f623 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -32,14 +32,15 @@ python3 -m http.server -d dist 8080
 ```
 
 Native CLI flags (`src/cli.rs`, applied in `FractalApp::apply_cli`): `--kind`,
-`--power`, `--julia re,im`, `--share <fragment>`,
+`--power`, `--julia re,im`, `--phoenix-p re,im`, `--lambda-l re,im`,
+`--palette`, `--share <fragment>`,
 `--view re,im,half_height[,iterations]`, `--de`, `--buddhabrot`,
-`--buddha-palette`, `--export` (+ `--export-path out.png`). `--headless`
-(`src/headless.rs`) skips the window entirely: it builds the same view from
-the other flags, creates its own offscreen wgpu device, and renders straight
-to a PNG (`--width`/`--height`, default 1920×1080) — implies `--export`'s
-save behavior without needing a GPU-backed window/event loop. Not yet
-supported with `--buddhabrot`. Run `mandelbrot --help` for the full list.
+`--buddha-palette`. `--headless` (`src/headless.rs`) skips the window
+entirely: it builds the same view from the other flags, creates its own
+offscreen wgpu device, and renders straight to a PNG (`--width`/`--height`,
+default 1920×1080, `--export-path out.png`) without needing a GPU-backed
+window/event loop. Not yet supported with `--buddhabrot`. Run
+`mandelbrot --help` for the full list.
 
 There's no GPU in most sandboxes: `cargo check`/`cargo test --test shader_valid`
 are the fast, headless way to validate a change. `cargo test` also runs but
diff --git a/src/app.rs b/src/app.rs
index 6048d42..550b794 100644
--- a/src/app.rs
+++ b/src/app.rs
@@ -327,7 +327,7 @@ pub struct FractalApp {
     export_requested: bool,
     /// Progress/handle for an in-flight PNG export, if any.
     export: Option<Arc<Mutex<ExportShared>>>,
-    /// Output path for `--export` (native CLI only); falls back to a
+    /// Output path for `--export-path` (native CLI only); falls back to a
     /// timestamped name when unset.
     export_path: Option<String>,
     /// Short status line (saved path, "link copied", errors).
@@ -500,6 +500,24 @@ impl FractalApp {
                 self.view = Self::default_view_for(FractalMode::Julia, self.kind);
             }
         }
+        if let Some(pp) = &cli.phoenix_p {
+            let p: Vec<&str> = pp.split(',').collect();
+            if let (Some(Ok(re)), Some(Ok(im))) = (
+                p.first().map(|s| s.trim().parse::<f64>()),
+                p.get(1).map(|s| s.trim().parse::<f64>()),
+            ) {
+                self.phoenix_p = (re, im);
+            }
+        }
+        if let Some(ll) = &cli.lambda_l {
+            let p: Vec<&str> = ll.split(',').collect();
+            if let (Some(Ok(re)), Some(Ok(im))) = (
+                p.first().map(|s| s.trim().parse::<f64>()),
+                p.get(1).map(|s| s.trim().parse::<f64>()),
+            ) {
+                self.lambda_l = (re, im);
+            }
+        }
         if let Some(frag) = cli.share
             && let Some(state) = ShareState::decode(&frag)
         {
@@ -517,10 +535,10 @@ impl FractalApp {
         if let Some(p) = cli.buddha_palette {
             self.buddha_palette = p.min(BUDDHA_PALETTE_NAMES.len() as u32 - 1);
         }
-        self.export_path = cli.export_path;
-        if cli.export {
-            self.export_requested = true;
+        if let Some(p) = cli.palette {
+            self.palette = p.min(PALETTE_NAMES.len() as u32 - 1);
         }
+        self.export_path = cli.export_path;
     }
 
     /// Apply a view spec "re,im,half_height[,iterations]" (re/im are decimal,
diff --git a/src/cli.rs b/src/cli.rs
index e2563ef..df5eb2c 100644
--- a/src/cli.rs
+++ b/src/cli.rs
@@ -25,6 +25,18 @@ pub struct Cli {
     #[arg(long, value_name = "RE,IM")]
     pub julia: Option<String>,
 
+    /// Coloring palette index.
+    #[arg(long, value_name = "INDEX")]
+    pub palette: Option<u32>,
+
+    /// Phoenix constant p for the Phoenix kind (z -> z^2 + c + p*z_prev).
+    #[arg(long, value_name = "RE,IM")]
+    pub phoenix_p: Option<String>,
+
+    /// Lambda constant λ for the Lambda kind (z -> λ*z*(1 - z)).
+    #[arg(long, value_name = "RE,IM")]
+    pub lambda_l: Option<String>,
+
     /// Restore a view from a share-link fragment (the part after '#').
     #[arg(long, value_name = "FRAGMENT")]
     pub share: Option<String>,
@@ -45,11 +57,7 @@ pub struct Cli {
     #[arg(long, value_name = "INDEX")]
     pub buddha_palette: Option<u32>,
 
-    /// Render a PNG export on startup.
-    #[arg(long)]
-    pub export: bool,
-
-    /// Output path for --export/--headless (default: fractal-<timestamp>.png).
+    /// Output path for --headless (default: fractal-<timestamp>.png).
     #[arg(long, value_name = "PATH")]
     pub export_path: Option<String>,