Algodoo

Made as best as i could, with phi precise to 6 digits.

What is a Penrose tiling:

Lets say you want to tile a plane - an infinite 2D space - with some set of tiles, which you choose beforehand. This isn't too hard. you can choose a square, triangle, or even a hexagon and easily fill the entire plane.

This will produce what is called a periodic pattern - if you make a copy of the plane out of glass, place it on the original, but shift it to the right a few tiles it will look exactly the same, no matter where you look.

Here's the challenge: choose your tiles such that you can tile the plane, but non-periodically, that is, if you make the glass copy, you could move it anywhere, but it wouldn't look the same. somewhere, even if kilometres far, the pattern wouldn't match.

The kite and the dart are one of these tiles, made by Roger Penrose in the 1970's. In the scene I've built a small part of it, but you can keep on adding pieces forever. However you have to follow some rules, the most important being:

Every corner/intersection must either complete the orange circle, or be completely empty, as it is in the scene. This rule can be enforced by making notches into the tiles, but this way its more pretty.

If you are confused and/or curious, check out this video on the topic:
https://youtu.be/48sCx-wBs34
Here is a nice animation showing the various properties and symmetries:
https://youtu.be/yK4P17Lsp2A?t=85