# Gilbert Tessellation

After some works on Gilbert Tessellations

I found some problems with my script, the logic was not very good to handle multiple cracks and curve in general (not just lines). It was quite long to find the good algorithm. Here is one version, that I am pretty happy with. Not very fast but it seems to work. The logic is quite simple.
Take curves, says that a curve represant the trajectory of a crack, this crack begins at the start point of the curve, it goes at constant velocity and continue until it touches another crack. As curves are finite I add an extension factor. If 0 no extension if 1 the extension has the length of the diagonal of the bounding box of all the input curves. I choose here to extend curves with line. It is easy to change it. And don’t forget curves are on XY planes and are projected on the XY plane inside the script.
So here a GH with simple script, and a ghuser (not possible to post ghuser). Note that Human plugin is not mandatory.
Gilbert Tessellation Example.gh (21.0 KB)

For a simple Gilbert Tessellation
Take some random point, with some random direction and propagrate the crack in 2 opposite directions

With a constant direction and multiple cracks

A serie with a palette choosen from a painting from a relative
https://www.instagram.com/p/BkPV0iXlUzx/?taken-by=kitou_art

Edit 24/06/2018
Some new tests

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Some new tessellations found answering this question

Some strange creatures emerging

I like a lot Rhino Rendered Mode, with some extrusion it gives some nice shades

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Great work, these patterns look amazing, and you can achieve lots of different looks from that definition.
Thanks for sharing.

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Some new Gilbert Tessellations applied on a mesh with variable speed. The initial curves are generated using geodesic curve on mesh.
Here
20 points which generates 3 rays each with a velocity of 200 (thick tubes)
and 100 points which generates 6 rays each with a velocity of 1 (thin tubes)

And the classic Tessellation, 2 fractures departing from the same point in opposite direction

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Beautiful! I have to study this.

Thanks Laurent, very stunning. Are you able to share the growth on mesh definition? Thanks!

Hello, I will not share my script. You will find geodesic curve on mesh here

Not sure it is will be easy to tweak, it is why I mainly prefer to make my own library in order to make what I want.

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Hello, I found some very nice implementation of Gilbert Tesselations by Parakeet @motaghi.esmaeil

They seems very similar () to what I posted here but they made some more integrated components.

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Hi dear Laurent
Thank your sincerely for checking out parakeet,
Indeed all of your creative works are source of inspiration for all of us. in this particular matter kindly note that:

• as I recall, in a discussion you described your method as ‘gradually growing curves from the points upuntil interesection occures’ on the other hand Parakeet’s method places all the curves regardless of intersections, gets the intersection events, sorts them to find to shatter curves in each cluster.
That said, for the sake of goodwill if you could send me an email (motaghi.esmaeil@gmail.com) i’ll send you the full script for this matter, if you decided there is meaningful similarity i’ll gladly include proper acknowledgements, it is absolutely your decision,
Best
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3D gilbert Tessellations on a sphere

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Bravo! Thanks for sharing! Always killing it!

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