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feat: add lambda fractal

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surv
2026-09-16 20:32:48 +02:00
parent 0b90b72a00
commit afcd3c74da
6 changed files with 276 additions and 103 deletions
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src/fractal/reference.rs
+98 -38
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@@ -18,37 +18,23 @@ use crate::view::{Big, big_from_f64};
#[derive(Clone, Copy, PartialEq, Eq, Debug)]
pub enum FractalKind {
/// `z -> z^2 + c`.
Mandelbrot,
Mandelbrot = 0,
/// `z -> (|Re z| + i|Im z|)^2 + c`.
BurningShip,
BurningShip = 1,
/// `z -> conj(z)^2 + c` (the Mandelbar).
Tricorn,
Tricorn = 2,
/// `z -> z^power + c` (power >= 2).
Multibrot,
Multibrot = 3,
/// `z -> |Re(z^2)| + i·Im(z^2) + c` (abs on the real output of the square).
Celtic,
Celtic = 4,
/// `z -> (x^2 - y^2) - 2·x·|y|·i + c` (abs on the imaginary input).
Perpendicular,
Perpendicular = 5,
/// `z -> |Re(z^2)| - |Im(z^2)|·i + c` (abs on both outputs).
Buffalo,
Buffalo = 6,
/// `z -> z^2 + c + p·z_{n-1}` (two-term recurrence; `p` is `phoenix_p`).
Phoenix,
}
impl FractalKind {
/// Integer id matching the shader's `KIND_*` constants.
pub fn shader_id(self) -> u32 {
match self {
FractalKind::Mandelbrot => 0,
FractalKind::BurningShip => 1,
FractalKind::Tricorn => 2,
FractalKind::Multibrot => 3,
FractalKind::Celtic => 4,
FractalKind::Perpendicular => 5,
FractalKind::Buffalo => 6,
FractalKind::Phoenix => 7,
}
}
Phoenix = 7,
/// `z -> lambda·z(1 - z)` (logistic map).
Lambda = 8,
}
/// Reference orbit escapes once |Z|^2 exceeds this. Kept larger than the pixel
@@ -70,6 +56,7 @@ pub fn compute_reference(
kind: FractalKind,
power: u32,
phoenix_p: (f64, f64),
lambda_l: (f64, f64),
) -> Vec<[f32; 2]> {
let cr = c_re.clone().with_precision(precision).value();
let ci = c_im.clone().with_precision(precision).value();
@@ -82,6 +69,9 @@ pub fn compute_reference(
// Phoenix distortion constant `p` (a small fixed complex number).
let pr = big_from_f64(phoenix_p.0, precision);
let pi = big_from_f64(phoenix_p.1, precision);
// Lambda distortion constant `l` (a small fixed complex number).
let lr = big_from_f64(lambda_l.0, precision);
let li = big_from_f64(lambda_l.1, precision);
let mut points: Vec<[f32; 2]> = Vec::with_capacity(max_iter as usize + 1);
@@ -144,6 +134,14 @@ pub fn compute_reference(
let pzi = &pr * &zi_prev + &pi * &zr_prev;
(re2 + &cr + pzr, im2 + &ci + pzi)
}
FractalKind::Lambda => {
// λ·z(1 - z): logistic map.
let re2 = 1 - &zr;
let im2 = -&zi;
let lzr = &lr * &zr - &li * &zi;
let lzi = &lr * &zi + &li * &zr;
(&lzr * &re2 - &lzi * &im2, re2 * lzi + lzr * im2)
}
};
// Shift the previous iterate (only the Phoenix arm reads it).
@@ -182,6 +180,7 @@ fn complex_pow(zr: &Big, zi: &Big, power: u32, precision: usize) -> (Big, Big) {
/// Convenience: parameter-plane ("Mandelbrot-set") reference (`z0 = 0`,
/// `c = center`) for any `kind`.
#[allow(clippy::too_many_arguments)]
pub fn compute_set_reference(
center_re: &Big,
center_im: &Big,
@@ -190,10 +189,11 @@ pub fn compute_set_reference(
kind: FractalKind,
power: u32,
phoenix_p: (f64, f64),
lambda_l: (f64, f64),
) -> Vec<[f32; 2]> {
let zero = big_zero(precision);
compute_reference(
&zero, &zero, center_re, center_im, max_iter, precision, kind, power, phoenix_p,
&zero, &zero, center_re, center_im, max_iter, precision, kind, power, phoenix_p, lambda_l,
)
}
@@ -207,8 +207,16 @@ mod tests {
fn reference_matches_naive_f64() {
let cr = Big::try_from(-0.75_f64).unwrap();
let ci = Big::try_from(0.1_f64).unwrap();
let points =
compute_set_reference(&cr, &ci, 60, 200, FractalKind::Mandelbrot, 2, (0.0, 0.0));
let points = compute_set_reference(
&cr,
&ci,
60,
200,
FractalKind::Mandelbrot,
2,
(0.0, 0.0),
(0.0, 0.0),
);
// Independent naive f64 orbit.
let (c_re, c_im) = (-0.75_f64, 0.1_f64);
@@ -238,8 +246,16 @@ mod tests {
fn interior_orbit_runs_full_length() {
let cr = Big::try_from(-0.2_f64).unwrap();
let ci = Big::try_from(0.0_f64).unwrap();
let points =
compute_set_reference(&cr, &ci, 500, 120, FractalKind::Mandelbrot, 2, (0.0, 0.0));
let points = compute_set_reference(
&cr,
&ci,
500,
120,
FractalKind::Mandelbrot,
2,
(0.0, 0.0),
(0.0, 0.0),
);
assert_eq!(points.len(), 501, "interior orbit should not escape");
}
@@ -248,8 +264,16 @@ mod tests {
fn burning_ship_reference_matches_naive_f64() {
let cr = Big::try_from(-1.75_f64).unwrap();
let ci = Big::try_from(-0.03_f64).unwrap();
let points =
compute_set_reference(&cr, &ci, 60, 200, FractalKind::BurningShip, 2, (0.0, 0.0));
let points = compute_set_reference(
&cr,
&ci,
60,
200,
FractalKind::BurningShip,
2,
(0.0, 0.0),
(0.0, 0.0),
);
let (c_re, c_im) = (-1.75_f64, -0.03_f64);
let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -269,8 +293,16 @@ mod tests {
fn multibrot3_reference_matches_naive_f64() {
let cr = Big::try_from(0.3_f64).unwrap();
let ci = Big::try_from(0.2_f64).unwrap();
let points =
compute_set_reference(&cr, &ci, 60, 200, FractalKind::Multibrot, 3, (0.0, 0.0));
let points = compute_set_reference(
&cr,
&ci,
60,
200,
FractalKind::Multibrot,
3,
(0.0, 0.0),
(0.0, 0.0),
);
let (c_re, c_im) = (0.3_f64, 0.2_f64);
let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -304,6 +336,7 @@ mod tests {
FractalKind::Mandelbrot,
2,
(0.0, 0.0),
(0.0, 0.0),
);
let (mut zr, mut zi) = (0.15_f64, -0.1_f64);
@@ -324,7 +357,16 @@ mod tests {
fn celtic_reference_matches_naive_f64() {
let cr = Big::try_from(-0.6_f64).unwrap();
let ci = Big::try_from(0.4_f64).unwrap();
let points = compute_set_reference(&cr, &ci, 60, 200, FractalKind::Celtic, 2, (0.0, 0.0));
let points = compute_set_reference(
&cr,
&ci,
60,
200,
FractalKind::Celtic,
2,
(0.0, 0.0),
(0.0, 0.0),
);
let (c_re, c_im) = (-0.6_f64, 0.4_f64);
let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -345,8 +387,16 @@ mod tests {
fn perpendicular_reference_matches_naive_f64() {
let cr = Big::try_from(-0.7_f64).unwrap();
let ci = Big::try_from(-0.2_f64).unwrap();
let points =
compute_set_reference(&cr, &ci, 60, 200, FractalKind::Perpendicular, 2, (0.0, 0.0));
let points = compute_set_reference(
&cr,
&ci,
60,
200,
FractalKind::Perpendicular,
2,
(0.0, 0.0),
(0.0, 0.0),
);
let (c_re, c_im) = (-0.7_f64, -0.2_f64);
let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -367,7 +417,16 @@ mod tests {
fn buffalo_reference_matches_naive_f64() {
let cr = Big::try_from(-1.2_f64).unwrap();
let ci = Big::try_from(-0.35_f64).unwrap();
let points = compute_set_reference(&cr, &ci, 60, 200, FractalKind::Buffalo, 2, (0.0, 0.0));
let points = compute_set_reference(
&cr,
&ci,
60,
200,
FractalKind::Buffalo,
2,
(0.0, 0.0),
(0.0, 0.0),
);
let (c_re, c_im) = (-1.2_f64, -0.35_f64);
let (mut zr, mut zi) = (0.0_f64, 0.0_f64);
@@ -389,7 +448,8 @@ mod tests {
let cr = Big::try_from(0.5667_f64).unwrap();
let ci = Big::try_from(0.0_f64).unwrap();
let p = (-0.5_f64, 0.0_f64);
let points = compute_set_reference(&cr, &ci, 60, 200, FractalKind::Phoenix, 2, p);
let points =
compute_set_reference(&cr, &ci, 60, 200, FractalKind::Phoenix, 2, p, (0.0, 0.0));
let (c_re, c_im) = (0.5667_f64, 0.0_f64);
let (mut zr, mut zi) = (0.0_f64, 0.0_f64);