You can read this paper for introduction: Paul Bourke - Random space filling of the plane (2011).
However, provided search algorithm for the next location is inefficient, and offers very limited control over the distribution. In this work, i present a new solver over discrete signed distance field:

Where sdf_n are custom signed distance functions. Aggregate minima of which is stored in a bitmap. c_n+1 marks a point with highest value of the field, which then supplied to the next iteration of the algorithm.

Currently, the solver is fully parallel, and highly generic. Supported: - Regular (fractal) distributions - Random distributions - Any shapes which can be represented with SDF: curves, regular polygons, non-convex polygons, disjoint areas - Mixed shapes.

Examples

You can run examples with following command:
cargo run --release --features "drawing" --example <example name> -- -C target-cpu=native

examples/fractal_distribution
Each subsequent circle is inserted at the maxima of distance field.

examples/random_distribution
Given (xy, value) of the maxima, a new random circle is inserted within a domain of radius value and center xy.

examples/embedded
A regular distribution embedded in a random one. 1. Insert a random distribution of circles; 1. Invert the distance field; 1. Insert a fractal distribution.

examples/polymorphic
Showcasing: - Dynamic dispatch interface; - Random distribution of mixed shapes; - Random color and texture fill style; - Parallel generation and drawing.

examples/image_dataset
Display over 100'000 images.
Run with cargo run --release --features "drawing" --example image_dataset -- "<image folder>" -C target-cpu=native

Past work

In src/legacy you can find numeruos algorithms which are worth re-exploring, including quadtree and GPU implementations.

Future work

• Add more sample SDFs, and generic draw trait
• Extend to discretization below 2^-16 (gigapixel resolution)

Once above are done, I will use this library for my next project "Gallery of Babel".