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feat: Add complex multibrot fractal

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This commit is contained in:
surv
2026-09-20 13:37:33 +02:00
parent c7d687c107
commit 06b52fe954
10 changed files with 311 additions and 19 deletions
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src/app.rs
+60 -6
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@@ -56,6 +56,7 @@ const KINDS: &[(FractalKind, &str)] = &[
(FractalKind::Buffalo, "Buffalo"),
(FractalKind::Phoenix, "Phoenix"),
(FractalKind::Lambda, "Lambda"),
(FractalKind::ComplexMultibrot, "Complex Multibrot"),
];
/// UI label for a fractal kind.
@@ -69,8 +70,8 @@ fn kind_label(kind: FractalKind) -> &'static str {
/// The iteration formula for a kind, in human-readable notation (mirrors the
/// doc comments on `FractalKind`'s variants). `power` is only used by
/// Multibrot.
fn kind_formula(kind: FractalKind, power: u32) -> String {
/// Multibrot; `complex_power` only by Complex Multibrot.
fn kind_formula(kind: FractalKind, power: u32, complex_power: (f64, f64)) -> String {
match kind {
FractalKind::Mandelbrot => "z = z² + c".to_string(),
FractalKind::BurningShip => "z = (|Re(z)| + i|Im(z)|)² + c".to_string(),
@@ -81,13 +82,16 @@ fn kind_formula(kind: FractalKind, power: u32) -> String {
FractalKind::Buffalo => "z = |Re(z²)| − i|Im(z²)| + c".to_string(),
FractalKind::Phoenix => "z = z² + c + p·z_prev".to_string(),
FractalKind::Lambda => "z = λ·z(1 − z)".to_string(),
FractalKind::ComplexMultibrot => {
format!("z = z^({:.3}{:+.3}i) + c", complex_power.0, complex_power.1)
}
}
}
type JuliaPreset = (&'static str, f64, f64, u32, Option<(f64, f64)>);
/// Nice-looking Julia constants offered as presets.
const JULIA_PRESETS: [&[JuliaPreset]; FractalKind::Lambda as usize + 1] = [
const JULIA_PRESETS: [&[JuliaPreset]; FractalKind::ComplexMultibrot as usize + 1] = [
&[
("dendrite", -0.8, 0.156, 400, None),
("rabbit", -0.123, 0.745, 400, None),
@@ -106,6 +110,7 @@ const JULIA_PRESETS: [&[JuliaPreset]; FractalKind::Lambda as usize + 1] = [
("archipelago 2", -0.556, 0.253, 500, Some((-0.415, -0.267))),
],
&[],
&[],
];
type SetPreset = (
@@ -120,7 +125,7 @@ type SetPreset = (
/// Curated beautiful locations offered as one-click presets.
/// Each is `(name, center_re, center_im, half_height, iterations)`; the centers
/// are decimals parsed at full precision so deep places stay sharp.
const SET_PRESETS: [&[SetPreset]; FractalKind::Lambda as usize + 1] = [
const SET_PRESETS: [&[SetPreset]; FractalKind::ComplexMultibrot as usize + 1] = [
&[
(
"Seahorse Valley",
@@ -171,6 +176,7 @@ const SET_PRESETS: [&[SetPreset]; FractalKind::Lambda as usize + 1] = [
Some((-0.9, -0.49)),
)],
&[],
&[],
];
/// Parameters a reference orbit was (or will be) computed for. Used to decide
@@ -186,6 +192,7 @@ struct RequestKey {
iter: u32,
kind: FractalKind,
power: u32,
complex_power: (f64, f64),
}
/// Shared state for an in-progress PNG export. The worker (a background thread
@@ -273,6 +280,8 @@ pub struct FractalApp {
kind: FractalKind,
/// Exponent for the Multibrot kind.
power: u32,
/// Complex exponent for the Complex Multibrot kind (`z^power + c`).
complex_power: (f64, f64),
julia_c: (f64, f64),
/// Distortion constant `p` for the Phoenix kind (`z^2 + c + p·z_{n-1}`).
phoenix_p: (f64, f64),
@@ -452,6 +461,7 @@ impl FractalApp {
mode: FractalMode::Mandelbrot,
kind: FractalKind::Mandelbrot,
power: 3,
complex_power: (2.0, 0.5),
julia_c: (-0.8, 0.156),
phoenix_p: (-0.5, 0.0),
lambda_l: (-0.5, 0.0),
@@ -513,6 +523,15 @@ impl FractalApp {
if let Some(p) = cli.power {
self.power = p.clamp(2, 8);
}
if let Some(cp) = &cli.complex_power {
let p: Vec<&str> = cp.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.complex_power = (re, im);
}
}
self.view = Self::default_view_for(self.mode, self.kind);
}
if let Some(jc) = cli.julia {
@@ -618,6 +637,7 @@ impl FractalApp {
julia_c: self.julia_c,
phoenix_p: self.phoenix_p,
lambda_l: self.lambda_l,
complex_power: self.complex_power,
color_scale: self.color_scale,
color_offset: self.color_offset,
palette: self.palette,
@@ -637,6 +657,7 @@ impl FractalApp {
self.julia_c = s.julia_c;
self.phoenix_p = s.phoenix_p;
self.lambda_l = s.lambda_l;
self.complex_power = s.complex_power;
self.color_scale = s.color_scale;
self.color_offset = s.color_offset;
self.palette = (s.palette as usize).min(PALETTE_NAMES.len() - 1) as u32;
@@ -688,6 +709,7 @@ impl FractalApp {
FractalKind::Buffalo => (-0.5, -0.5, 1.5),
FractalKind::Phoenix => (0.0, 0.0, 1.6),
FractalKind::Lambda => (0.0, 0.0, 1.6),
FractalKind::ComplexMultibrot => (0.0, 0.0, 1.5),
};
ViewState::with_center(big_from_f64(cr, 53), big_from_f64(ci, 53), hh)
}
@@ -704,6 +726,7 @@ impl FractalApp {
iter: self.max_iterations,
kind: self.kind,
power: self.power,
complex_power: self.complex_power,
}
}
@@ -729,6 +752,7 @@ impl FractalApp {
|| key.iter != self.max_iterations
|| key.kind != self.kind
|| key.power != self.power
|| key.complex_power != self.complex_power
{
return true;
}
@@ -797,6 +821,7 @@ impl FractalApp {
power: key.power,
phoenix_p: key.phoenix_p,
lambda_l: key.lambda_l,
complex_power: key.complex_power,
});
self.pending = true;
}
@@ -816,6 +841,7 @@ impl FractalApp {
key.power,
key.phoenix_p,
key.lambda_l,
key.complex_power,
)
} else {
compute_set_reference(
@@ -827,6 +853,7 @@ impl FractalApp {
key.power,
key.phoenix_p,
key.lambda_l,
key.complex_power,
)
};
self.apply_reference(
@@ -881,6 +908,7 @@ impl FractalApp {
key.power,
key.phoenix_p,
key.lambda_l,
key.complex_power,
)
} else {
compute_set_reference(
@@ -892,6 +920,7 @@ impl FractalApp {
key.power,
key.phoenix_p,
key.lambda_l,
key.complex_power,
)
};
self.apply_reference(
@@ -921,6 +950,7 @@ impl FractalApp {
dc_offset: self.dc_offset(),
phoenix_p: [self.phoenix_p.0 as f32, self.phoenix_p.1 as f32],
lambda_l: [self.lambda_l.0 as f32, self.lambda_l.1 as f32],
complex_power: [self.complex_power.0 as f32, self.complex_power.1 as f32],
de_coloring: (self.de_coloring | self.shadow) as u32,
shadow: self.shadow as u32,
_pad: [0; _],
@@ -941,6 +971,7 @@ impl FractalApp {
aspect: aspect as f32,
phoenix_p: [self.phoenix_p.0 as f32, self.phoenix_p.1 as f32],
lambda_l: [self.lambda_l.0 as f32, self.lambda_l.1 as f32],
complex_power: [self.complex_power.0 as f32, self.complex_power.1 as f32],
bailout_sq: BAILOUT_SQ,
kind: self.kind as u32,
power: self.power,
@@ -954,7 +985,7 @@ impl FractalApp {
height: 0, // set by the callback from size_px
total_samples: 0.0, // tracked by the renderer across frames
palette: self.buddha_palette,
_pad: [0; 3],
_pad0: 0,
}
}
@@ -1246,6 +1277,12 @@ impl FractalApp {
self.lambda_l.0, self.lambda_l.1
));
}
if self.kind == FractalKind::ComplexMultibrot {
ui.label(format!(
"power = {:.6} {:+.6}i",
self.complex_power.0, self.complex_power.1
));
}
ui.separator();
ui.label(self.kind.description());
@@ -1270,7 +1307,8 @@ impl FractalApp {
ui.label(
"A deep-zoom fractal explorer. It renders the Mandelbrot set \
and several related fractals (Burning Ship, Tricorn, \
Multibrot, Celtic, Perpendicular, Buffalo, Phoenix, Lambda).",
Multibrot, Complex Multibrot, Celtic, Perpendicular, Buffalo, \
Phoenix, Lambda).",
);
ui.add_space(4.0);
ui.label(
@@ -1511,6 +1549,22 @@ impl FractalApp {
ui.label("i");
});
}
if self.kind == FractalKind::ComplexMultibrot {
ui.horizontal(|ui| {
ui.label("power =");
ui.add(
egui::DragValue::new(&mut self.complex_power.0)
.speed(0.01)
.range(-8.0..=8.0),
);
ui.add(
egui::DragValue::new(&mut self.complex_power.1)
.speed(0.01)
.range(-8.0..=8.0),
);
ui.label("i");
});
}
if self.kind != prev_kind {
self.view = Self::default_view_for(self.mode, self.kind);
}