Wolfram Research

Minimal Inequivalent Square Tilings

Source Notebook

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

Originator: Stephen Wolfram

Details

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.

Examples

Basic Examples

Retrieve the default content:

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

Choose 3 tilings at random:

In[2]:=
RandomSample[ResourceData[
ResourceObject["Minimal Inequivalent Square Tilings"]], 3][All, "TilingImage"]
Out[2]=

Find the tilings with the most black cells:

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

Wolfram Research, "Minimal Inequivalent Square Tilings" from the Wolfram Data Repository (2021) https://doi.org/10.24097/wolfram.00988.data

Data Resource History

Source Metadata

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