EASY MATH TESSELLATION HOW TO
EASY MATH TESSELLATION SERIES

Every time I begin working with these patterns I'm constantly amazed by them.Īpparently Keith Critchlow an artist, lecturer, author, and professor of architecture, has made extensive studies in Islamic architecture, arts and decoration, and I've ordered a couple of books written by him, Order in Space and Islamic Patterns: An Analytical and Cosmological Approach, to further my own education on this topic. It seems that using circle construction of a grid of equilateral triangles, this pattern can be discovered, along with numerous variations, eg:Īfter working with this and other Islamic patterns I find that this not only appeals to the viewer but as much to the artist. Within the confines of my limited research, it seems that geometric designs in Islamic art hold no specific religious significance (I expect this is a highly controversial statement.) and instead provide an opportunity for craftsmen to demonstrate the skill and subtlety of their workmanship, and to dazzle and intrigue the viewer with their complexity. Well, it turns out that this specific pattern:Īppears originally in Islamic / Arabic / Moorish art. However, this statement was pure speculation based on the appearance of similar patterns in Chinese art, also using the p31m wallpaper tiling method, this one below for example. Previously I'd said, (I believe the pattern is pretty old and of Chinese origin.). Additional notes on the origin of this pattern. I know that this doesn't help too much in understanding less rigid tessellation designs, such as Escher's reptiles, which I assume MCE made intuitively (I read that he wasn't a mathematician, which I was surprised by.)Īnyway, I hope this question isn't too sprawling, and thank you for looking.

EASY MATH TESSELLATION HOW TO

How to construct the shape unit mathematically.

How to calculate the relative positions of each shape to build the grid programmatically.

There appears to be a equilateral triangle which contains the key dimensions, and of course the regular hexagon is important, since this essentially forms 2 interwoven hexagonal grids.īeyond this I'm unable to express mathematically what is going on. Here's some examples of patterns I've worked up.īecause I don't really understand the math, I've had to create the basic unit shape by hand, I can see the 60/120 degree angles well enough, but I really want to figure out the proportions of the shape, which appear (from just looking) to be tightly interrelated.Ī few observations I've made during this process (aside from it being a bit more tricky than I first imagined.)

EASY MATH TESSELLATION SERIES

In my spare time, I'm playing a lot with a series of patterns which use a hexagonal grid, and a tessellating design I saw on a chair in my dentist's surgery. Tessellation is fascinating to me, and I've always been amazed by the drawings of M.C.Escher, particularly interesting to me, is how he would've gone about calculating tessellating shapes.

Easy math tessellation