All these tiles exhibit "golden ratio" properties. This is an interesting subject to contemplate, even if you're not a mathematician. Gary Meisner has an entire wonderful website, Golden Number, devoted to just this subject, exploring the manifestations of golden properties throughout nature. His description of Penrose tiles is especially attractive and easy to understand.

Such tiles also have a propensity for "non-periodic" tilings. These are arrangements of tiles that fill the plane in such a way that there are no regularly recurring patterns. The same-looking cluster of tiles can recur infinitely often, but not evenly spaced apart. It takes a whole lot of tiles to lay out a big enough arrangement to observe this phenomenon.

You can lay out and discover all kinds of interesting features and patterns with Stephen Collins' software, "Bob." Bob is a Microsoft Windows program designed to produce and explore rhombic Penrose tilings that form an infinite, aperiodic plane. See it and download it from his website, Patterns within Rhombic Penrose Tiling.

Jay Bonner of Santa Fe, NM, is a specialist in classic Islamic tilings and has created many new designs based on their techniques. He uses them in his architectural work and has written a book on their historical development and traditional methods. See how beautiful they are.

And if you'd like to try some online pattern-making of your own with virtual tiles, including pentagons, visit Tyler Art Gallery to admire, and download the Tyler Java applet to play.