80 lines
2.5 KiB
Rust
80 lines
2.5 KiB
Rust
|
use nalgebra::{SMatrix, SVector};
|
||
|
|
use linregress::{FormulaRegressionBuilder, RegressionDataBuilder};
|
||
|
|
|
||
|
|
type Matrix4 = SMatrix<f64, 4, 4>;
|
||
|
|
type Vector4 = SVector<f64, 4>;
|
||
|
|
|
||
|
|
fn search(generators: &Vec<Matrix4>, root: Vector4, upper_bound: f64) -> usize {
|
||
|
|
let mut current = vec![(root, 5)];
|
||
|
|
let mut next = vec![];
|
||
|
|
let mut total = 0;
|
||
|
|
loop {
|
||
|
|
next.clear();
|
||
|
|
for (tuple, previous_generator) in ¤t {
|
||
|
|
for (i, generator) in generators.iter().enumerate() {
|
||
|
|
let new_tuple = generator * tuple;
|
||
|
|
if !(i == 0 && *previous_generator == 3) && !(i == 1 && *previous_generator == 2) && i != *previous_generator && new_tuple[i] < upper_bound && new_tuple.iter().sum::<f64>() > tuple.iter().sum() {
|
||
|
|
next.push((new_tuple, i));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
if current.is_empty() {
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
total += next.len();
|
||
|
|
std::mem::swap(&mut current, &mut next);
|
||
|
|
}
|
||
|
|
2 * (total + root.len())
|
||
|
|
}
|
||
|
|
|
||
|
|
fn fractal_dimension(generators: Vec<Matrix4>, root: Vector4, upper_bound: f64, n: isize) -> Result<f64, linregress::Error> {
|
||
|
|
let xs: Vec<f64> = (1..=n).map(|x| (x as f64 * upper_bound / (n as f64)).ln()).collect();
|
||
|
|
let ys: Vec<f64> = xs.iter().map(|upper_bound| (search(&generators, root, upper_bound.exp()) as f64).ln()).collect();
|
||
|
|
|
||
|
|
let data = vec![("Y", ys), ("X", xs)];
|
||
|
|
let data = RegressionDataBuilder::new().build_from(data)?;
|
||
|
|
|
||
|
|
let formula = "Y ~ X";
|
||
|
|
let model = FormulaRegressionBuilder::new()
|
||
|
|
.data(&data)
|
||
|
|
.formula(formula)
|
||
|
|
.fit()?;
|
||
|
|
|
||
|
|
let parameters = model.parameters;
|
||
|
|
Ok(parameters.regressor_values[0])
|
||
|
|
}
|
||
|
|
|
||
|
|
fn main() {
|
||
|
|
let generators = vec![
|
||
|
|
Matrix4::new(
|
||
|
|
-1.0, 2.0, 2.0, 0.0,
|
||
|
|
0.0, 1.0, 0.0, 0.0,
|
||
|
|
0.0, 0.0, 1.0, 0.0,
|
||
|
|
0.0, 0.0, 0.0, 1.0,
|
||
|
|
),
|
||
|
|
Matrix4::new(
|
||
|
|
1.0, 0.0, 0.0, 0.0,
|
||
|
|
2.0, -1.0, 0.0, 2.0,
|
||
|
|
0.0, 0.0, 1.0, 0.0,
|
||
|
|
0.0, 0.0, 0.0, 1.0,
|
||
|
|
),
|
||
|
|
Matrix4::new(
|
||
|
|
1.0, 0.0, 0.0, 0.0,
|
||
|
|
0.0, 1.0, 0.0, 0.0,
|
||
|
|
2.0, 0.0, -1.0, 2.0,
|
||
|
|
0.0, 0.0, 0.0, 1.0,
|
||
|
|
),
|
||
|
|
Matrix4::new(
|
||
|
|
1.0, 0.0, 0.0, 0.0,
|
||
|
|
0.0, 1.0, 0.0, 0.0,
|
||
|
|
0.0, 0.0, 1.0, 0.0,
|
||
|
|
0.0, 2.0, 2.0, -1.0,
|
||
|
|
),
|
||
|
|
];
|
||
|
|
|
||
|
|
let root = Vector4::new(-2., 4., 5., 9.);
|
||
|
|
|
||
|
|
println!("{}", fractal_dimension(generators, root, 10_000_000.0, 50).unwrap());
|
||
|
|
}
|