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```use math;
use math::{Point2, Point3, Point4};
use noise_fns::{MultiFractal, NoiseFn, Perlin, Seedable};
use std;

/// Noise function that outputs fBm (fractal Brownian motion) noise.
///
/// fBm is a _monofractal_ method. In essence, fBm has a _constant_ fractal
/// dimension. It is as close to statistically _homogeneous_ and _isotropic_
/// as possible. Homogeneous means "the same everywhere" and isotropic means
/// "the same in all directions" (note that the two do not mean the same
/// thing).
///
/// The main difference between fractal Brownian motion and regular Brownian
/// motion is that while the increments in Brownian motion are independent,
/// the increments in fractal Brownian motion depend on the previous increment.
///
/// fBm is the result of several noise functions of ever-increasing frequency
/// and ever-decreasing amplitude.
///
/// fBm is commonly referred to as Perlin noise.
#[derive(Clone, Debug)]
pub struct Fbm {
/// Total number of frequency octaves to generate the noise with.
///
/// The number of octaves control the _amount of detail_ in the noise
/// function. Adding more octaves increases the detail, with the drawback
/// of increasing the calculation time.
pub octaves: usize,

/// The number of cycles per unit length that the noise function outputs.
pub frequency: f64,

/// A multiplier that determines how quickly the frequency increases for
/// each successive octave in the noise function.
///
/// The frequency of each successive octave is equal to the product of the
/// previous octave's frequency and the lacunarity value.
///
/// A lacunarity of 2.0 results in the frequency doubling every octave. For
/// almost all cases, 2.0 is a good value to use.
pub lacunarity: f64,

/// A multiplier that determines how quickly the amplitudes diminish for
/// each successive octave in the noise function.
///
/// The amplitude of each successive octave is equal to the product of the
/// previous octave's amplitude and the persistence value. Increasing the
/// persistence produces "rougher" noise.
pub persistence: f64,

seed: u32,
sources: Vec<Perlin>,
}

impl Fbm {
pub const DEFAULT_SEED: u32 = 0;
pub const DEFAULT_OCTAVE_COUNT: usize = 6;
pub const DEFAULT_FREQUENCY: f64 = 1.0;
pub const DEFAULT_LACUNARITY: f64 = std::f64::consts::PI * 2.0 / 3.0;
pub const DEFAULT_PERSISTENCE: f64 = 0.5;
pub const MAX_OCTAVES: usize = 32;

pub fn new() -> Self {
Self {
seed: Self::DEFAULT_SEED,
octaves: Self::DEFAULT_OCTAVE_COUNT,
frequency: Self::DEFAULT_FREQUENCY,
lacunarity: Self::DEFAULT_LACUNARITY,
persistence: Self::DEFAULT_PERSISTENCE,
sources: super::build_sources(Self::DEFAULT_SEED, Self::DEFAULT_OCTAVE_COUNT),
}
}
}

impl Default for Fbm {
fn default() -> Self {
Self::new()
}
}

impl MultiFractal for Fbm {
fn set_octaves(self, mut octaves: usize) -> Self {
if self.octaves == octaves {
return self;
}

octaves = math::clamp(octaves, 1, Self::MAX_OCTAVES);
Self {
octaves,
sources: super::build_sources(self.seed, octaves),
..self
}
}

fn set_frequency(self, frequency: f64) -> Self {
Self { frequency, ..self }
}

fn set_lacunarity(self, lacunarity: f64) -> Self {
Self { lacunarity, ..self }
}

fn set_persistence(self, persistence: f64) -> Self {
Self {
persistence,
..self
}
}
}

impl Seedable for Fbm {
fn set_seed(self, seed: u32) -> Self {
if self.seed == seed {
return self;
}

Self {
seed,
sources: super::build_sources(seed, self.octaves),
..self
}
}

fn seed(&self) -> u32 {
self.seed
}
}

/// 2-dimensional Fbm noise
impl NoiseFn<Point2<f64>> for Fbm {
fn get(&self, mut point: Point2<f64>) -> f64 {
let mut result = 0.0;

point = math::mul2(point, self.frequency);

for x in 0..self.octaves {
// Get the signal.
let mut signal = self.sources[x].get(point);

// Scale the amplitude appropriately for this frequency.
signal *= self.persistence.powi(x as i32);

// Add the signal to the result.
result += signal;

// Increase the frequency for the next octave.
point = math::mul2(point, self.lacunarity);
}

// Scale and shift the result into the [-1,1] range
let scale = 2.0 - self.persistence.powi(self.octaves as i32 - 1);
result / scale
}
}

/// 3-dimensional Fbm noise
impl NoiseFn<Point3<f64>> for Fbm {
fn get(&self, mut point: Point3<f64>) -> f64 {
let mut result = 0.0;

point = math::mul3(point, self.frequency);

for x in 0..self.octaves {
// Get the signal.
let mut signal = self.sources[x].get(point);

// Scale the amplitude appropriately for this frequency.
signal *= self.persistence.powi(x as i32);

// Add the signal to the result.
result += signal;

// Increase the frequency for the next octave.
point = math::mul3(point, self.lacunarity);
}

// Scale and shift the result into the [-1,1] range
let scale = 2.0 - self.persistence.powi(self.octaves as i32 - 1);
result / scale
}
}

/// 4-dimensional Fbm noise
impl NoiseFn<Point4<f64>> for Fbm {
fn get(&self, mut point: Point4<f64>) -> f64 {
let mut result = 0.0;

point = math::mul4(point, self.frequency);

for x in 0..self.octaves {
// Get the signal.
let mut signal = self.sources[x].get(point);

// Scale the amplitude appropriately for this frequency.
signal *= self.persistence.powi(x as i32);

// Add the signal to the result.
result += signal;

// Increase the frequency for the next octave.
point = math::mul4(point, self.lacunarity);
}

// Scale and shift the result into the [-1,1] range
let scale = 2.0 - self.persistence.powi(self.octaves as i32 - 1);
result / scale
}
}
```