Struct MandelbrotSet 

pub struct MandelbrotSet {
    pub max_iter: u32,
    pub escape_radius_sq: f64,
}

The Mandelbrot set: z_{n+1} = z_n^2 + c, starting from z_0 = 0.

Points c in the complex plane are classified by the escape time of the orbit {z_n}.

Fields

max_iter: u32

Maximum number of iterations before declaring a point in the set.

escape_radius_sq: f64

Escape radius squared.

Implementations

impl MandelbrotSet

pub fn new(max_iter: u32, escape_radius: f64) -> Self

Create a new Mandelbrot set with given parameters.

pub fn default_set() -> Self

Default Mandelbrot set with max_iter=256, escape_radius=2.

pub fn escape_time(&self, cr: f64, ci: f64) -> Option<u32>

Compute escape time for a complex number c = (cr, ci).

Returns None if the orbit does not escape within max_iter iterations, or Some(iterations) with the escape iteration count.

pub fn smooth_escape_time(&self, cr: f64, ci: f64) -> f64

Smooth escape time using renormalization.

Returns a continuous (smooth) iteration count for coloring.

pub fn is_in_set(&self, cr: f64, ci: f64) -> bool

Check if a point is in the Mandelbrot set.

pub fn is_boundary(&self, cr: f64, ci: f64, delta: f64) -> bool

Detect if a point is near the boundary of the set.

A point is near the boundary if it is in the set but has a neighbor that is not (or vice versa), within the given delta distance.

pub fn area_monte_carlo( &self, x_min: f64, x_max: f64, y_min: f64, y_max: f64, num_samples: usize, ) -> f64

Compute the area of the Mandelbrot set using Monte Carlo sampling.

Samples random points in the rectangle [x_min, x_max] x [y_min, y_max] and estimates the area as the fraction of points in the set times the rectangle area.

pub fn render_grid( &self, x_min: f64, x_max: f64, y_min: f64, y_max: f64, width: usize, height: usize, ) -> Vec<Vec<Option<u32>>>

Generate a grid of escape times for rendering.

Returns a row-major width x height grid of escape times.