wallswitch 0.60.12

//! Newton-Raphson Basin fractal generator overlay.
//!
//! This module implements the Relaxed Newton-Raphson fractal for solving complex polynomial
//! equations of the form z^p - 1 = 0. By introducing a complex relaxation parameter (lambda),
//! the standard basins of attraction warp into intricate, symmetric, mandala-like
//! structures featuring nested circular bands, spiral arms, and crystalline structures.

use crate::{
    ColorRGB, Complex, FractalConfig, FractalDescriptor, MAX_ITERATIONS, MIN_ITERATIONS, Monitor,
    NEON_PALETTES, RelaxedEscape, RelaxedViewportConfig, get_random_integer,
    optimize_relaxed_viewport,
};

/// Valid operational range for randomized zoom viewport allocation.
const ZOOM_RANGE: [f64; 2] = [1.5, 3.8];

/// Structural parameters for polynomial evaluation and deformation.
///
/// Holds the power p of the equation z^p - 1 = 0, the relaxation parameter lambda,
/// and a user-friendly preset name.
#[derive(Debug, Clone, Copy, PartialEq)]
pub struct NewtonPreset {
    /// Power of the polynomial.
    pub power: u32,
    /// Complex relaxation scale parameter.
    pub lambda: Complex,
    /// Human-readable name of the specific layout.
    pub name: &'static str,
}

/// A procedural generator for rendering Newton-Raphson Basin fractals onto backgrounds.
pub struct NewtonGenerator {
    /// Active parameters governing formula geometry.
    pub preset: NewtonPreset,
    /// Shared viewport layout configuration.
    pub config: FractalConfig,
}

impl Default for NewtonGenerator {
    fn default() -> Self {
        Self {
            preset: NewtonPreset {
                power: 3,
                lambda: Complex::new(1.0, 0.3),
                name: "Gothic Rose Mandala",
            },
            config: FractalConfig {
                scan_iterations: get_random_integer::<_, u32>(
                    MIN_ITERATIONS / 10,
                    MAX_ITERATIONS / 10,
                )
                .max(60),
                color_palette: NEON_PALETTES[0],
                zoom: 2.0,
                rotation: Complex::one(),
            },
        }
    }
}

impl FractalDescriptor for NewtonGenerator {
    #[inline(always)]
    fn config(&self) -> &FractalConfig {
        &self.config
    }

    #[inline(always)]
    fn center(&self) -> Complex {
        Complex::zero()
    }

    #[inline(always)]
    fn is_julia(&self) -> bool {
        true
    }

    #[inline(always)]
    fn render_pixel(&self, z_init: Complex, _scale: f64, max_radius: f64) -> (ColorRGB, f64, f64) {
        let (i, diff_norm, z_final) = compute_newton_escape(
            z_init,
            self.preset.power,
            self.preset.lambda,
            self.config.scan_iterations,
        );

        // Circular edge fade utilizing Complex's native circular_fade directly in f64
        let edge_fade = z_init.circular_fade(max_radius, 0.40);
        let escape_state = RelaxedEscape {
            iterations: i,
            max_iterations: self.config.scan_iterations,
            diff_norm,
            z_final,
        };
        escape_state.color(self.config.color_palette, edge_fade, (1e-6_f64).ln(), false)
    }

    fn info_text(&self) -> String {
        format!(
            "fractal [{}]\n\
            f(z) = z^{} - 1 = 0, where lambda = {:5.2} {:+4.2}i (iter = {:4}, zoom = {:.2}), color: {}",
            self.preset.name,
            self.preset.power,
            self.preset.lambda.re,
            self.preset.lambda.im,
            self.config.scan_iterations,
            self.config.zoom,
            self.config.color_palette
        )
    }
}

impl NewtonGenerator {
    /// Generates a randomized Newton Basin configuration fitted to the aspect ratio.
    pub fn random(monitor: &Monitor) -> Self {
        let presets = [
            NewtonPreset {
                power: 3,
                lambda: Complex::new(1.0, 0.3),
                name: "Gothic Rose Mandala",
            },
            NewtonPreset {
                power: 5,
                lambda: Complex::new(0.9, 0.1),
                name: "Imperial Star Compass",
            },
            NewtonPreset {
                power: 4,
                lambda: Complex::new(1.0, 0.0),
                name: "Stained Glass Kaleidoscope",
            },
            NewtonPreset {
                power: 6,
                lambda: Complex::new(0.85, 0.2),
                name: "Cosmic Snowflake Grid",
            },
            NewtonPreset {
                power: 3,
                lambda: Complex::new(1.35, 0.0),
                name: "Spiked Crown of Thorns",
            },
            NewtonPreset {
                power: 8,
                lambda: Complex::new(0.7, 0.4),
                name: "Quantum Energy Shells",
            },
            NewtonPreset {
                power: 5,
                lambda: Complex::new(1.1, 0.25),
                name: "Solar Flare Compass",
            },
            NewtonPreset {
                power: 3,
                lambda: Complex::new(0.8, 0.5),
                name: "Celtic Knotwork Ribbon",
            },
            NewtonPreset {
                power: 4,
                lambda: Complex::new(0.6, 0.6),
                name: "Nautilus Spiral Chamber",
            },
            NewtonPreset {
                power: 7,
                lambda: Complex::new(1.0, 0.05),
                name: "Hyper-Dimensional Matrix",
            },
            NewtonPreset {
                power: 6,
                lambda: Complex::new(1.15, 0.15),
                name: "Aetheric Frost Flower",
            },
            NewtonPreset {
                power: 8,
                lambda: Complex::new(0.90, 0.30),
                name: "Celestial Gearwork",
            },
            NewtonPreset {
                power: 3,
                lambda: Complex::new(0.75, 0.60),
                name: "Byzantine Dome",
            },
            NewtonPreset {
                power: 5,
                lambda: Complex::new(1.25, -0.20),
                name: "Abyssal Starfish",
            },
            NewtonPreset {
                power: 4,
                lambda: Complex::new(0.80, 0.45),
                name: "Hyperborean Sigil",
            },
            NewtonPreset {
                power: 7,
                lambda: Complex::new(1.0, -0.30),
                name: "Prismatic Labyrinth",
            },
            NewtonPreset {
                power: 3,
                lambda: Complex::new(0.95, 0.80),
                name: "Nebula Core Spiral",
            },
            NewtonPreset {
                power: 5,
                lambda: Complex::new(0.60, 0.80),
                name: "Aura Borealis Compass",
            },
            NewtonPreset {
                power: 10,
                lambda: Complex::new(0.85, 0.0),
                name: "Obsidian Glass Lattices",
            },
            NewtonPreset {
                power: 4,
                lambda: Complex::new(1.40, -0.40),
                name: "Bio-Polymer Filament",
            },
        ];

        let p_idx: usize = get_random_integer(0, NEON_PALETTES.len() - 1);
        let color_palette = NEON_PALETTES[p_idx];

        let angle_degrees: f64 = get_random_integer(0, 359);
        let radians = angle_degrees.to_radians();

        let preset_idx: usize = get_random_integer(0, presets.len() - 1);
        let selected_preset = presets[preset_idx];

        let mut newton = Self {
            preset: selected_preset,
            config: FractalConfig {
                scan_iterations: get_random_integer(40, 100),
                color_palette,
                zoom: 2.0,
                rotation: Complex::from_polar(1.0, radians),
            },
        };

        newton.optimize_fit(monitor);
        newton
    }

    /// Automatically scales the viewport boundaries with randomized micro-deviations.
    pub fn optimize_fit(&mut self, monitor: &Monitor) {
        let width = monitor.resolution.width as u32;
        let height = monitor.resolution.height as u32;

        let scan_iterations = self.config.scan_iterations;
        let power = self.preset.power;
        let lambda = self.preset.lambda;

        let config = RelaxedViewportConfig {
            width,
            height,
            search_limit: 1.8,
            steps: 64,
            zoom_range: ZOOM_RANGE,
            rand_range: [0.95, 1.25],
            fallback_range: [1.50, 2.50],
        };

        let (zoom, rotation) = optimize_relaxed_viewport(config, self.config.rotation, |z| {
            let (i, _, _) = compute_newton_escape(z, power, lambda, scan_iterations);
            i > 2 && i < scan_iterations - 2
        });

        self.config.zoom = zoom;
        self.config.rotation = rotation;
    }
}

/// Evaluates polynomial convergence under a relaxed Newton-Raphson iteration loop.
#[inline(always)]
fn compute_newton_escape(
    z_init: Complex,
    power: u32,
    lambda: Complex,
    scan_iterations: u32,
) -> (u32, f64, Complex) {
    let mut z = z_init;
    let mut i = 0;
    let mut diff_norm = 1.0;

    while i < scan_iterations {
        if z.abs_sq() < 1e-8 {
            break;
        }

        let step = lambda * z.newton_step_term(power);
        let z_next = z - step;

        diff_norm = step.abs_sq();
        if diff_norm < 1e-6 {
            z = z_next;
            break;
        }

        z = z_next;
        i += 1;
    }

    (i, diff_norm, z)
}

#[cfg(test)]
mod tests_newton {
    use super::*;

    #[test]
    fn test_newton_generation_random() {
        let monitor = Monitor::default();
        let newton = NewtonGenerator::random(&monitor);
        assert!(newton.config.zoom > 0.0);
        assert!(newton.config.scan_iterations > 0);
    }
}