Roly.jl (Reverse-Search Polyform Enumerator) is a Julia package for the enumeration of arbitrary polyforms via reverse search. It allows you to exhaustively enumerate structures composed out of a set of arbitrarily shaped building blocks in 2D or 3D and provides an interface to define your own building block geometries and binding rules. Roly.jl is under active development, and breaking changes can occur at any time. Because of its depencencies, Roly.jl currently requires a POSIX operating system (this requirement will be lifted in the future).
To install Roly.jl and its dependencies directly from your Julia REPL, first press ] to enter Pkg mode, and then run
pkg> add https://github.com/mxhbl/Roly.jl
Structure enumeration in Roly.jl starts from an AssemblySystem, which is a list of building block geometries together with an interaction matrix that specificies which binding site of which building block are allowed to bind.
The allowed structures can then be enumerated with the function polyenum, or generated and stored with polygen.
To illustrate the basic process, let's construct an assembly system consisting of four species of triangular building blocks. You can define the binding rules via a matrix, where every row defines an allowed bond in the form [species_i site_i species_j site_j]. For example, the row [1 3 2 3] indicates that site 3 of species 1 is allowed to bind to site 3 of species 2. Roly already comes with definitions for simple polygonal and polyhedral building block geometries, allowing us to specify e.g. triangular building blocks via a UnitTriangleGeometry. The AssemblySystem constructor takes either a list of geometries or a single geometry if all building blocks are identically shaped.
using Roly
bonds = [1 3 2 3;
2 2 3 2;
2 1 4 1;
3 1 4 1]
asys = AssemblySystem(bonds, UnitTriangleGeometry)
Once you have defined an assembly system, you can use polyenum to enumerate all possible structures:
n_strs, largest_strsize = polyenum(asys; max_size=20, max_strs=100_000)
The simple system we have chosen here only allows 16 different structures to form. In general however, the number of structures might be unbounded and it is advisable to always impose either a maximal structure size (max_size), or maximal number of structures (max_strs) to be enumerated. In addition, polyenum allows the user to pass functions for processing, selectively storing, or rejecting structures.
If you want to store all possible structures in memory for further processing, you can either use polyenum with an aggregation function, or use polygen. polygen stores all structures in memory, making it less memory efficient than polyenum.
polygen uses the same interface as polyenum, but simply returns a list of structures:
strs = polygen(asys; max_size=20, max_strs=100_000)
To visualize 2D structures, use RolyVis.jl:
using RolyVis
draw_polyforms(strs, asys, "filename.pdf//png")
If you use Roly.jl in your work, please cite the paper below.
@article{roly2024,
title={Accessing Semi-Addressable Self Assembly with Efficient Structure Enumeration},
author={Maximilian C. H\"ubl and Carl P. Goodrich},
year={2024},
eprint={2405.13567},
archivePrefix={arXiv},
}