13
$\begingroup$

Does anyone know if there's a client or web app that generates Penrose patterns which can then be converted to a tileable rectangular background image for web site?

I found this http://stephencollins.net/penrose but I can't seem to get a rectangular shape out of it for web use. Thanks.

$\endgroup$
  • $\begingroup$ Just crop it !! $\endgroup$ – Yves Daoust Jul 26 '15 at 11:55
  • $\begingroup$ This question is one of those questions that can provoke true insight in a subject :) (when answered properly and with some effort of the questioner to really try to understand what they were asking) $\endgroup$ – hopla May 4 at 15:16
16
$\begingroup$

I believe, since Penrose tilings are aperiodic (lacking translational symmetry), there isn't such a rectangular shape.

$\endgroup$
  • $\begingroup$ That's too bad. But I can see why it's not feasible. $\endgroup$ – Jin Oct 24 '10 at 5:00
  • 1
    $\begingroup$ @Jin Then again, various lobbies and rooms across the world have been tiled with Penrose tiles. Some of these places are probably rectangular or roughly so. Also the kite and dart Penrose pattern uses rhombuses, and thus are angled such that a rectangular space could be filled (if the rules allow). $\endgroup$ – ben May 6 '14 at 5:49
  • 1
    $\begingroup$ Being able to fill a rectangular region is different from creating a tileable rectangle (a rectangle for which opposite edges can be glued together to continue the pattern seamlessly). $\endgroup$ – Isaac Jul 22 '15 at 18:09
1
$\begingroup$

I found this java software that exports as PNG. You cannot tile it, just use an image.

$\endgroup$
1
$\begingroup$

Only dragging up an old post because there's still something more to do -- if you want a penrose tiling as a background, I built one a while ago that will generate an image for your purpose:

https://github.com/etisab/penrosetiler

Of course the tiles don't fit perfectly into a rectangle (they are clipped at the edges), it should work just fine as a pretty background image.

$\endgroup$
0
$\begingroup$

here is a shadertoy program for 5 axis quasi symmetry pics, it's not as tileable as a tile version.

I just wrote a program to investigate 5 fold symmetry in 2d, it generates something akin to penrose tiling. here is a pic enter image description here and a video on YT:

i am not convinced that it can't practically be tiled in a square shape, you may have places where only one triangle is wrong in a frame of 1000 of them or something, else you could find a place with good 4 fold symmetry and blur some small places where is different on the edge.

$\endgroup$
0
$\begingroup$

I found this page, it generates an SVG image: https://craftdesignonline.com/penrose/

$\endgroup$

protected by J. M. is a poor mathematician Jul 30 '16 at 13:19

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.