### Mahvish Nagda – Project3 – Generating Tile Patterns

by mahvish @ 9:02 am 28 February 2012

Inspiration

My goal with this project from the proposal: The idea was to use Arabic tiling patterns that are well established and use that for some generative form. I grew up in the Middle East so saw these beautiful patterns everywhere. I also think there is potential for something generative in the mathematics behind these patterns.

I spent the majority of my learning about the math behind these patterns and their relationship to quasicrystals (so potentially self similar patterns). I found a paper that describes a method to create self similar patterns. My current goal is to implement a parameterized version of that method, and then play with the parameters to see what happens. I can also use this as a library to combine to get other affects.

Specific notations: {10|3} for star polygons

Algorithms

Considered geomerative & point2D libraries but PVector was good enough. I’m not at that point yet, but I think I might be using L-systems further down the line.

Image from Paper

Screenshots

Look at slideshow.

References

The global long-range order of quasi-periodic patterns in Islamic architecture

Decagonal and Quasi-crystalline Tilings in Medieval Islamic Architecture

Tilings and Patterns

Moving forward

Interlace Patterns in Islamic & Moorish Art

Quasi-Crystals and Geometry

Specific directions forward: space filling algorithms (around the red stars), making it repeat at different levels, or making this 3d (link & link). This can then be used for for some sort of printing like here.

## 1 Comment

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Wang Tiling! Theres a siggraph paper on it. Fractals also work .

These remind me of Mandalas now, and theres been some interesting work generatively creating those. (http://lgo900.wordpress.com/2011/06/04/html-5-sacred-geometry-generator-with-sample-images/) popped up on google that focuses on equations.

I think you’re making this way more complicated than you need to. Especially for the mesh forms, you can definitely use toxiclibs to do really simple mesh subdivision that creates that highly ordered/repetitive pattern, and then its really easy to export to the 3D printer!
The colored images are really pretty, but I’m not entirely clear on how they’re generated. I wonder if you could have made an animated GIF as an easy way to illustrate the generation of these shapes.

what’s your motivation? trying to replicate these types of pattern algorithmically only? how can you adapt the scheme or merge it with other systems/patterns/cultures to synthesize something new (ok you said spherical 3d mesh version–that could look really nice, especially as a 3d printed object)

yea i’m not sure how to tie the generative nature of your program into the purpose of these designs, i feel like putting a pattern on ti might take away from the end result, but is defintely very interesting to see that the pattern match so well. i guess it won’t really be clear how it feels to look at thema nd compare until you have a tangibke output, so keep going with it and see what you find.

I really like the concentric circles image in your blog post. There’s a very elegant simplicity to it. From a purely visual perspective, I think this image and some of the other experiments with stars are actually nicer than some the the more pattern-centric output.

nice reflection on possible improvements.

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I’m not well-versed on Islamic mosaics, but this seems a fertile ground for some provocative exploration on the relationship between Faith and Mathematics+1, mediated by computation.

Would be really great if you could fit these patterns to a shape (like an arch) rather than just radial patterns.

+1 to letterpressed prints! Definitely would be good to produce some physical product at the end of this project.

It would be cool to replicate your algorithm in Grasshopper and create some computational Islamic architecture

You really dissected these patterns and it is really neat to see your process and how you explored an observation you made long ago. I think that is an awesome adventure in itself!

Nice personal inspiration. This patterning is broken down extensively in art/architecture history texts. Super interesting. http://www.amazon.com/Power-Limits-Proportional-Harmonies-Architecture/dp/0877731934 Field trip: Dubai I’m in. Can we stay in the hotel with the tennis court helipad?Yes, we can.

the new shot looks much more natural of a tiling pattern.

I think you are successful in way you created bunch of different patterns using an algorithm. I like the images you just showed ( the printed patterns). I guess you can develop the project more in depth and print it in 3D form later. It will look beautiful!

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I love your inspiration. It’s beautiful.

it is interesting how a lot of the patterns you made look like portals/holes.

Seems like there’s a lot to know in order to generate these patterns accurately.

Might be interesting to use your processing code to generate PDF’s, which are then lasercut from some kind of acrylic or other plastic material — some kind of physical output.

I think, like with Alex Wolfe’s project, these would be great if they were made into some physical form and context. I think this would set your patterns apart from the sources you’re drawing inspiration from.
Seems like you found a lot of great information on this subject.

how about putting the mesh into the node of the mesh…….infinity……

could be nice if they were on a color background instead of white, i think it give the compositions more weight

Great inspiration, it’s really interesting how much complexity there is.

Print it out! might be 3D printed

Great exploration.

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Comment by dan — 28 February 2012 @ 8:14 pm