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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[\!\(\* TagBox["\"\<Minimal Inequivalent Square Tilings\>\"", #& , BoxID -> "ResourceTag-Minimal Inequivalent Square Tilings-Input", AutoDelete->True]\)]
Out[1]=

Choose 3 tilings at random:

In[2]:=
RandomSample[ResourceData[\!\(\* TagBox["\"\<Minimal Inequivalent Square Tilings\>\"", #& , BoxID -> "ResourceTag-Minimal Inequivalent Square Tilings-Input", AutoDelete->True]\)], 3][All, "TilingImage"]
Out[2]=

Find the tilings with the most black cells:

In[3]:=
ResourceData[\!\(\* TagBox["\"\<Minimal Inequivalent Square Tilings\>\"", #& , BoxID -> "ResourceTag-Minimal Inequivalent Square Tilings-Input", AutoDelete->True]\)][ TakeSmallestBy[ Mean[Flatten[ImageData[ColorConvert[#TilingImage, GrayLevel]]]] & , 3], {"ConstraintNumber", "TilingImage"}]
Out[3]=

Wolfram Research, "Minimal Inequivalent Square Tilings" from the Wolfram Data Repository (2022)   https://doi.org/10.24097/wolfram.00988.data

Data Resource History

  • Date Created:

Source Metadata

  • Citation: Stephen Wolfram "A New Kind of Science" (2002)

Publisher Information

  • Prepared for the Wolfram Data Repository By: Stephen Wolfram
  • Publisher of Record: Wolfram Research