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Random Close Packing Algorithm

A custom particle packing algorithm was developed (based on a method proposed by Xu et al.1) to generate random close packings of hard disks in 2D and hard spheres in 3D. The algorithm is available for download and has been used as the foundation for subsequent packing studies.

Algorithm Overview

The procedure relies on an iterative swell–contract–minimize cycle:

  1. Initialize a random arrangement of non-overlapping particles.
  2. Gradually swell all particles until overlaps appear.
  3. Apply energy minimization to remove overlaps (move particles to nearest non-overlapping configuration).
  4. If energy minimization succeeds, swell again; otherwise contract particles and retry.
  5. Repeat, slowly decreasing the swell/contract step size, until a jammed (RCP) configuration is reached.
Animation showing the RCP algorithm evolving: particles swell, overlap, then minimize energy repeatedly until a jammed configuration is reached

Animation of the algorithm in action — particles (shown as disks) swell, develop overlaps, and are repositioned by energy minimization. The cycle repeats with a decreasing step size until a random close packing is reached.

Flowchart of the RCP generation algorithm

Flowchart illustrating the swell–contract–minimize procedure.

Example 2D random close packing of binary disks

An example random close packing of binary 2D disks generated by the algorithm.

This algorithm can produce both monodisperse and polydisperse sphere and disk packings, and has been extended to confined geometries (see Confined RCP).

3 K. W. Desmond and E. R. Weeks, “Influence of particle size distribution on random close packing of spheres,” Physical Review E 90, 022204 (2014). View paper.

2 K. W. Desmond and E. R. Weeks, “Random close packing of disks and spheres in confined geometries,” Physical Review E 80, 051305 (2009). View paper.

3 N. Xu, J. Blawzdziewicz, and C.S. O'Hern, “Influence of particle size distribution on random close packing of spheres,” Physical Review E 71, 061306 (2005). View paper.

Interactive packing app

🧪 Open the interactive packing app

RCPGenerator interactive 2D packing app
Explore how the pressure like μ term and ADAM learning rate affect a two-dimensional particle packing.

The hosted app is an interactive 2D demonstration of the a newer packing process (citation below). Choose the number of particles, initial packing fraction, and diameter distribution; generate an initial periodic packing; and then run or stop the ADAM-based relaxation directly in the browser.

While the packing runs, the μ and learning-rate sliders can be adjusted in real time. This makes it possible to explore how the particle-growth control and optimization step size affect overlaps, energy, packing fraction, and the evolution of the configuration. The resulting particle positions and diameters can be downloaded as a CSV file.

The app is intended for interactive exploration and education. It is a browser-based 2D implementation and is separate from the maintained rcpgenerator Python package and its compiled numerical engine.

4 K. Desmond, “Random close packing at extreme size ratios with an Adam-based inflation protocol,” arXiv:2608.12235 (2026). View paper.

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