sphere-packing

Toolbox for particulate microstructure modelling

A high volume fraction sphere packing library

benchmark solutions for selected packing problems: circle, rectangle, cube, cuboid, polygon packings

Monte Carlo simulation of hard sphere packing using MATLAB

Fast Python, C++ & MATLAB code to generate random close packings (or jammed, overlapping or dense packing as well), such as dense 2d disk packings, dense 3d sphere packings with generalization to hypersphere N dimensional packings.

Finding the dense packing structure of hard spheres in cylindrical pores by sequential linear programming (SLP) mthod.

These scripts can be used to draw spheres and points on a sphere.

Collection of personal Unity projects

A new way to teach higher mathematics by classifying its paradoxes, not resolving them: the integers 0–9 as shapes (the base, from the book The Shape of Understanding), the towers of higher math they point up to, and the coin — two sides and an edge — on every floor. Machine-checked; an earlier AI-built table program is archived with its audit.

Lean 4 proof that the kissing number of three-dimensional space is 12

Hard drives make up a system of many particles, so we can approach the dynamics from a statistical point of view. The following model is based on the game of stones.

Byte-exact theorems on the Fermat quartic fourfold lattice — from a run at the unbeaten dimension-128 sphere-packing record. Keystone: the Bridge Theorem (Hodge norm = geometric intersection form).

This repository contains the code to reproduce the results presented in the paper following paper: *N. Diaz, A. Alvarado, P. Meza, F. Guzman and E. Vera, "Multispectral Filter Array Design by Optimal Sphere Packing," in Transactions on Image Processing, 2023.

GPU-accelerated sphere packing of watertight triangle meshes using CUDA

First independent byte-exact reproduction of the Zinoviev-Ericson (1999) K(13) = 1154 kissing configuration in R^13, with full optimization pipeline, 13 paper-grade structural findings on dim-13 saturation, rare-paths doctrine, and dual Constructor/Auditor methodology with both-hats discipline.

Proof of Cohn and Rajagopal's Conjecture 3.1: six-dimensional kissing configurations containing Q5 or R5 have at most 70 points. Manuscript and exact verification.

Random sphere packings in Python: exact event-driven Lubachevsky-Stillinger algorithm (C++20 core), jamming protocol, packed tubes, structure analysis

One drawing, followed all the way down: incentre construction, uniform honeycombs, borides, rigidity in n dimensions, and open agent-assisted research tracks

6,071 new best-known packings of equal circles, spheres and hyperspheres (Packomania, 21 tables: triangle, quadrant, semicircle, rectangles, square, 5-, 6-, 15- and 16-gon, spheres in a cube and a sphere, balls in 4-6 D), each verified by two independent exact checkers; 1,340 certified locally optimal. By Moki&Julio.