Octagon - Square Tesselation

Hi Guys,

I'm working on an islamic pattern based on octagon and squares, the way this is constructed is that the 2 shapes are related by mathematical formulas and then subdivided and morphed etc.

now I need to manipulate the space in between them, how can I achieve this?

Replies to This Discussion

Permalink Reply by Joseph Oster on June 24, 2015 at 7:16am

This doesn't directly answer your question... It's a Syrian tile pattern that has long fascinated me:

Attachments:

syrian_tile_2015Jun7a.gh, 18 KB

Permalink Reply by Kim hauer on June 24, 2015 at 5:46pm

It may not be the answer David is looking for.

Nevertheless this is a very creative tile pattern... Nice work!

Permalink Reply by Joseph Oster on July 28, 2015 at 11:24am

It has to be at least ten years ago that I saw this pattern behind Syrian "President" Assad standing at a podium - and it showed up again today on Huffington Post...

Permalink Reply by cristo on July 23, 2015 at 5:01pm

Hi David

I am actually working on a similar project, and I am facing a similar problem with my pattern, the geometry your referring to is called by some academics " joining geometry" translated from french "géométrie de raccordement" this geometry is different and unique to each pattern, and is highly dependent on the central geometry of the pattern, some non exhaustive rules imply that:

this geometry is usualy the extension of the central one
follow by the preceding rule the same angularity than the central geometry
the angles are dictated by the parent geometry shape, here you have an octogon, which means that the angles are either or both the ( subdivision usually) and multiplication of the PI/2.rad angle(90°, 45°, 22.5° and so on)
there is the notion of tiling, which also dictactes the axes of symmetry and possible combination of primary shapes , here you've got the (4,8,8) tiling, which goes along with what is called an octocagonal symmetry

What you've got here is the base geometry, that you could fill with a variety of rich ornaments, I suggest You look at Jule's bourgoin book : "Les éléments de l'art arabe : le trait des entrelacs " there you may find your pattern in a higher complexity and diversity, if you come to analyse them, you could figure out the logical relationships between the shapes , or what you're referring to "mathematical formula"

I think finding some patterns of reference is the best way to tacle even more complex shapes

If you want more insights at least about some academic works I will be pleased to share my humble gathering of knowledge

Good luck

Permalink Reply by Kim hauer on July 25, 2015 at 3:10pm

I'm throwing my hat in the ring with my limited experience. I drew the geometry I was interesting in quickly in SketchUp. In Grasshooper I'm joining the geometry between a decagon and a pentagon using the list item comp, then I created a new surface between the 2 shapes . I'm not sure now what the next step is no in generating a repeating pattern?

Attachments:

islamic.gh, 16 KB

Permalink Reply by ng5 Alex on July 25, 2015 at 4:57pm

Hello David,

i thought i give it a try.

cheers

alex

Permalink Reply by ng5 Alex on July 25, 2015 at 5:57pm

Attachments:

octa_ag.gh, 22 KB

Permalink Reply by Kim hauer on July 26, 2015 at 11:53am

Hi Alex:

thanks once again, I now see I'm in serious need of some series configuration :)

regardless, I think your syrian tile is creatively the BEST!

Permalink Reply by Kim hauer on July 26, 2015 at 1:59pm

Yikes! ... sorry Alex I have to give the credit back to Joseph for the syrian tile, my bad!

Will you please take 2nd Best? :) I have always had the idea to replace the dbl entry door for my house with an Islamic motive.

In addition there is a very complex relationship between the 2 main geometric shapes, which are fighting for the same space, as one gets smaller the other gets larger, as one changes in the numbers of segments in one, the 2nd one has to react accordingly, or vice versa. This is not an easy exercise, which I can wrap my head around, since there are so many solutions.

Permalink Reply by ng5 Alex on July 26, 2015 at 7:28pm

Hey Kim no worries,

its not like there's a first or second for me. i just solved through grasshopper a geometric pattern, like it has been described by the OP. Though if i had to choose, i really like the Syrian one too.

cheers

alex

Permalink Reply by Joseph Oster on July 26, 2015 at 12:20pm

Alex - Well done! Very beautiful. Amazing.

Permalink Reply by ng5 Alex on July 26, 2015 at 12:43pm

thank you!,

check out nfold blog, might be of interest. full of patterns

the previous definition was loosely based on an older answer in this thread.

cheers

alex