Wolfram Research

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.

Examples

Basic Examples

Retrieve the resource:

In[1]:=
ResourceObject["c9d8f65c-66d4-4025-9840-f1d8647ae5ad"]
Out[1]=

Retrieve the default content:

In[2]:=
ResourceData["c9d8f65c-66d4-4025-9840-f1d8647ae5ad"]
Out[2]=

Choose 3 tilings at random:

In[3]:=
RandomSample[ResourceData["c9d8f65c-66d4-4025-9840-f1d8647ae5ad"], 3][All, "TilingImage"]
Out[3]=

Find the tilings with the most black cells:

In[4]:=
ResourceData["c9d8f65c-66d4-4025-9840-f1d8647ae5ad"][
 TakeSmallestBy[
  Mean[Flatten@ImageData[ColorConvert[#TilingImage, GrayLevel]]] &, 3],
 {"ConstraintNumber", "TilingImage"}
 ]
Out[4]=
In[5]:=

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

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