9804

Quadrilateral Tiling with Textures

This Demonstration tiles the plane with textures defined from portions of an image. Controls are provided to select the location and magnification within the image for use in the tiling. The shape of the tiling can be changed by clicking inside the image area. It may be more convenient to work with a small portion of the full tiling (uncheck "tile image area") and to then adjust the image. Clicking the "tile image area" button retiles the image area.
The construction begins with an arbitrary quadrilateral with vertices , , , and . These four points can be changed by clicking (and dragging) in the image area. Clicking close to one of the vertices causes that vertex to relocate to the mouse position; dragging the vertex causes the quadrilateral to continuously resize.

The tiling begins by rotating the quadrilateral 180 degrees around the midpoint of each side. For example, the starting position in the image area shows a misshaped rectangle. This shape is rotated 180 degrees around the midpoint of the line segment connecting and , once around the midpoint of the side connecting and , once around the midpoint of the line connecting and , and once around the midpoint of the line connecting and . Now the original shape can be translated by and by to fill in the gaps. The construction can be repeated to fill up the whole plane, and it works for any quadrilateral, even those that are nonconvex.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+