166 lines
7.3 KiB
Rust
166 lines
7.3 KiB
Rust
//! `FractalKind`: the enum selecting which iteration formula is in use, plus
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//! everything that only needs to switch on it (UI label/description/formula
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//! text, share-link tag, default parameter-plane view). The CPU/GPU orbit
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//! math itself lives in `reference.rs` (CPU reference orbit) and
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//! `shaders/mandelbrot.wgsl` (GPU perturbation delta) since both must also
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//! stay in sync with `common.wgsl`'s `KIND_*` constants.
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/// The iteration formula. Must be kept in sync with `advance_delta` and the
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/// `KIND_*` constants in the shader.
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#[repr(u8)]
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#[derive(Clone, Copy, PartialEq, Eq, Debug)]
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pub enum FractalKind {
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/// `z -> z^2 + c`.
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Mandelbrot = 0,
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/// `z -> (|Re z| + i|Im z|)^2 + c`.
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BurningShip = 1,
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/// `z -> conj(z)^2 + c` (the Mandelbar).
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Tricorn = 2,
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/// `z -> z^power + c` (power >= 2).
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Multibrot = 3,
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/// `z -> |Re(z^2)| + i·Im(z^2) + c` (abs on the real output of the square).
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Celtic = 4,
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/// `z -> (x^2 - y^2) - 2·x·|y|·i + c` (abs on the imaginary input).
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Perpendicular = 5,
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/// `z -> |Re(z^2)| - |Im(z^2)|·i + c` (abs on both outputs).
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Buffalo = 6,
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/// `z -> z^2 + c + p·z_{n-1}` (two-term recurrence; `p` is `phoenix_p`).
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Phoenix = 7,
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/// `z -> lambda·z(1 - z)` (logistic map).
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Lambda = 8,
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/// `z -> z^power + c`, where `power` is a complex constant (the
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/// `complex_power` argument), via the principal branch `z^p = exp(p·ln z)`.
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ComplexMultibrot = 9,
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}
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impl FractalKind {
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/// Every kind, in declaration/discriminant order. Sized arrays keyed by
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/// `kind as usize` (`JULIA_PRESETS`, `SET_PRESETS`) must have one slot per
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/// entry here.
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pub const ALL: [FractalKind; 10] = [
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FractalKind::Mandelbrot,
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FractalKind::BurningShip,
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FractalKind::Tricorn,
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FractalKind::Multibrot,
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FractalKind::Celtic,
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FractalKind::Perpendicular,
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FractalKind::Buffalo,
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FractalKind::Phoenix,
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FractalKind::Lambda,
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FractalKind::ComplexMultibrot,
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];
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pub fn description(&self) -> &'static str {
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match self {
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FractalKind::Mandelbrot => {
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"The Mandelbrot set is the most famous fractal set, obtained with the simplest escape-time formula. This set represents all Julia fractals: each points of the Mandelbrot set is related to a specific Julia fractal."
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}
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FractalKind::BurningShip => {
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"A variation of the famous Mandelbrot set, using absolute values on the real and imaginary part of each iterations."
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}
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FractalKind::Tricorn => {
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"The Tricorn set is obtained using the same formula as the Mandelbrot set, taking the complex conjugate of the previous iteration."
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}
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FractalKind::Multibrot => {
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"Multibrot use the same formula as the Mandelbrot set, with a bigger exposant."
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}
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FractalKind::Celtic => "",
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FractalKind::Perpendicular => "",
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FractalKind::Buffalo => "",
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FractalKind::Phoenix => "",
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FractalKind::Lambda => "",
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FractalKind::ComplexMultibrot => {
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"Like Multibrot, but the exponent itself is a complex number instead of a plain integer, via z^p = exp(p·ln z)."
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}
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}
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}
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/// UI label for this kind (combo box / info panel heading).
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pub fn label(&self) -> &'static str {
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match self {
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FractalKind::Mandelbrot => "Mandelbrot",
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FractalKind::BurningShip => "Burning Ship",
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FractalKind::Tricorn => "Tricorn",
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FractalKind::Multibrot => "Multibrot",
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FractalKind::Celtic => "Celtic",
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FractalKind::Perpendicular => "Perpendicular",
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FractalKind::Buffalo => "Buffalo",
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FractalKind::Phoenix => "Phoenix",
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FractalKind::Lambda => "Lambda",
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FractalKind::ComplexMultibrot => "Complex Multibrot",
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}
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}
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/// The iteration formula in human-readable notation (mirrors the doc
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/// comments on the variants above). `power` is only used by Multibrot;
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/// `complex_power` only by Complex Multibrot.
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pub fn formula(&self, power: u32, complex_power: (f64, f64)) -> String {
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match self {
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FractalKind::Mandelbrot => "z = z² + c".to_string(),
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FractalKind::BurningShip => "z = (|Re(z)| + i|Im(z)|)² + c".to_string(),
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FractalKind::Tricorn => "z = conj(z)² + c".to_string(),
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FractalKind::Multibrot => format!("z = z^{power} + c"),
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FractalKind::Celtic => "z = |Re(z²)| + i·Im(z²) + c".to_string(),
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FractalKind::Perpendicular => "z = (x² − y²) − 2x|y|i + c".to_string(),
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FractalKind::Buffalo => "z = |Re(z²)| − i|Im(z²)| + c".to_string(),
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FractalKind::Phoenix => "z = z² + c + p·z_prev".to_string(),
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FractalKind::Lambda => "z = λ·z(1 − z)".to_string(),
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FractalKind::ComplexMultibrot => {
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format!("z = z^({:.3}{:+.3}i) + c", complex_power.0, complex_power.1)
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}
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}
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}
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/// Short tag used to identify this kind in a share-link fragment.
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pub fn share_tag(&self) -> &'static str {
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match self {
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FractalKind::Mandelbrot => "mandel",
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FractalKind::BurningShip => "burning",
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FractalKind::Tricorn => "tricorn",
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FractalKind::Multibrot => "multi",
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FractalKind::Celtic => "celtic",
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FractalKind::Perpendicular => "perp",
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FractalKind::Buffalo => "buffalo",
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FractalKind::Phoenix => "phoenix",
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FractalKind::Lambda => "lambda",
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FractalKind::ComplexMultibrot => "cmulti",
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}
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}
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/// Inverse of `share_tag`; unknown tags fall back to `None` so the caller
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/// can decide the default (matches historical share-link behavior).
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pub fn from_share_tag(tag: &str) -> Option<FractalKind> {
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Some(match tag {
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"mandel" => FractalKind::Mandelbrot,
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"burning" => FractalKind::BurningShip,
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"tricorn" => FractalKind::Tricorn,
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"multi" => FractalKind::Multibrot,
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"celtic" => FractalKind::Celtic,
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"perp" => FractalKind::Perpendicular,
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"buffalo" => FractalKind::Buffalo,
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"phoenix" => FractalKind::Phoenix,
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"lambda" => FractalKind::Lambda,
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"cmulti" => FractalKind::ComplexMultibrot,
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_ => return None,
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})
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}
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/// Default parameter-plane (Mandelbrot-mode) view for this kind, as
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/// `(center_re, center_im, half_height)`. The Julia (dynamical) plane
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/// doesn't vary by kind, so it isn't covered here.
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pub fn default_set_view(&self) -> (f64, f64, f64) {
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match self {
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FractalKind::Mandelbrot => (-0.5, 0.0, 1.25),
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FractalKind::BurningShip => (-0.5, -0.5, 1.3),
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FractalKind::Tricorn => (-0.25, 0.0, 1.6),
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FractalKind::Multibrot => (0.0, 0.0, 1.5),
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FractalKind::Celtic => (-0.5, 0.0, 1.6),
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FractalKind::Perpendicular => (-0.5, 0.0, 1.5),
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FractalKind::Buffalo => (-0.5, -0.5, 1.5),
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FractalKind::Phoenix => (0.0, 0.0, 1.6),
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FractalKind::Lambda => (0.0, 0.0, 1.6),
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FractalKind::ComplexMultibrot => (0.0, 0.0, 1.5),
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}
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}
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}
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