/ Plots / 179 "squares packing 001"

Packing rotated squares in a square. Black fountain pens on Bristol. Interestingly one square didn't draw due to ink issues. It makes the final art pretty unique!

Technical notes

The algorithm brute-forces with 1 million iterations to find square location, for each iteration it will then search for the biggest square that can fit in the location space. I didn't even implemented dichotomic search for finding the square scale (it's a simple loop) but the overall script runs relatively fast in Rustlang (less than 10 seconds).

main loop

let mut polys = Vec::new();
let mut rng = rng_from_seed(opts.seed);
for i in 0..1000000 {
    let x: f64 = rng.gen_range(bounds.0, bounds.2);
    let y: f64 = rng.gen_range(bounds.1, bounds.3);
    let a: f64 = rng.gen_range(0.0, 8.0);
    if let Some(size) = poly_square_scaling_search(bounds, &polys, x, y, a, min_threshold) {
        let poly = rotated_square_as_polygon(x, y, size - pad, a);
    if polys.len() > desired_count {


fn poly_square_scaling_search(
    boundaries: (f64, f64, f64, f64),
    polys: &Vec<Polygon<f64>>,
    x: f64,
    y: f64,
    angle: f64,
    min_threshold: f64
) -> Option<f64> {
    let mut size = 0.1;
    let dsize = 0.1;
    // TODO dichotomic search could help perf here...
    loop {
        let poly = rotated_square_as_polygon(x, y, size, angle);
        let bounds = poly.bounding_rect().unwrap();
        let topleft: Point<f64> = bounds.min().into();
        let bottomright: Point<f64> = topleft + point!(
            x: bounds.width(),
            y: bounds.height()
        if out_of_boundaries(topleft.x_y(), boundaries) || out_of_boundaries(bottomright.x_y(), boundaries) {
        if poly_collides_in_polys(polys, &poly) {
        size += dsize;
    if size < min_threshold {
        return None;
    return Some(size);
As a generative plotter artist, I use code to generate art (creative coding) and physically create it with pen plotters, which is itself a generative process – each physical plot is a unique variant. I love dualities, like digital vs analog physical, abstract vs figurative, orthogonal vs polar, photo vs noise,...