Readme:

A simple implementation of the deBuijn method for non periodic tilings of the plane.

Bruijn, de, N. G. (1981). Algebraic theory of Penrose's non-periodic tilings of the plane. Indagationes Mathematicae, 43(1), 39-66.

See also https://github.com/neozhaoliang/pywonderland/blob/master/src/aperiodic-tilings/debruijn.py for another implementation, much more "professional" and pythonic, but with a different display style.

Another valuable site : https://www.mathpages.com/home/kmath621/kmath621.htm

Preferred installation

source .venv/bin/activate
pip install -r requirements.txt

Usage

To run the script, use the following command:

python main.py -c <config_file_path> -g <function_name>

Arguments

• -c, --config: Path to the configuration file (default: configs/config_polo.json).
• -g, --go: Name of the function to run (default: goAllDefaults).
• -N, --N: lenght of gamma (default: 5).

Example

To run the script with a different configuration file and function, use the following command:

python main.py -c configs/config_mike.json -g goVerySmall

The demo

The following code:

python main.py -g goDemo

returns the following graph:

Glyphs

An example of function calling is:

python main.py -g goGlyphs

This will read the default config file. With a little trial and error, one can get this kind of graphs:

Neighbours

Neighbours, descriptions and parameters

Building on the precedent stream of work, the graph is extracted from the tiling. For each vertex of the graph, one draws a polygon that join, for each edge from the vertex, a point on this edge at distance k from the vertex.

By default, edges between the polygons are plotted. This can be changed with the "draw_edges" key in the config file.

By default, the distance k is 0.333. This can be changed with the "k" key in the config file.

See go_neighbours.py for implementation details.

Examples

An example of function calling is:

python main.py -g goNeighbours -c configs/config_polo_neighbours.json

Note that on the example above, there is no edge between the polygons. This is because in the config called, the key "draw_edges" is at "False".

One can also change the N via command line, for example:

python main.py -g goNeighbours -N 6