Minimal Inequivalent Square Tilings

A dataset of images and constraints for the minimal inequivalent square tilings, along with the allowed tiles that generate the tiling

Originator: Stephen Wolfram

This dataset was presented in its original form on pages 214 and 215 of Stephen Wolfram’s “A New Kind of Science”.

The function for generating a tiling from a constraint is also provided.

(5 columns, 171 rows)

Examples

Basic Examples

Retrieve the resource:

In[1]:=
ResourceObject["Minimal Inequivalent Square Tilings"]
Out[1]=

Retrieve the default content:

In[2]:=
ResourceData["Minimal Inequivalent Square Tilings"]
Out[2]=

Choose 3 tilings at random:

In[3]:=
RandomSample[ResourceData["Minimal Inequivalent Square Tilings"], 
  3][All, "TilingImage"]
Out[3]=

Find the tilings with the most black cells:

In[4]:=
ResourceData["Minimal Inequivalent Square Tilings"][
 TakeSmallestBy[
  Mean[Flatten@ImageData[ColorConvert[#TilingImage, GrayLevel]]] &, 3],
 {"ConstraintNumber", "TilingImage"}
 ]
Out[4]=

Wolfram Research, "Minimal Inequivalent Square Tilings" from the Wolfram Data Repository. (2017) https://doi.org/10.24097/wolfram.00988.data

Source Metadata

Data Downloads