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Developing fractal curves [message #50796] Wed, 04 July 2012 13:05 UTC Go to next message
avatar henryseg  is currently offline henryseg
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Registered: July 2008
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Here are two designs on the same theme, based on an idea originally due to Geoffrey Irving (who is involved in 3D printing, but isn't on Shapeways as far as I know). The idea is to show how the fractal curve is generated, by illustrating the iterative process as the curve gets more and more crinkly as a surface.

Shapeways pages:
Developing dragon curve
Developing Hilbert curve

Videos:
Developing dragon curve
Developing Hilbert curve

index.php?t=getfile&id=18196&private=0
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index.php?t=getfile&id=18200&private=0
index.php?t=getfile&id=18197&private=0
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Re: Developing fractal curves [message #50800 is a reply to message #50796 ] Wed, 04 July 2012 14:17 UTC Go to previous messageGo to next message
avatar Wahtah is currently online Wahtah
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I love them! Brilliant... That's it really, just saying...
Re: Developing fractal curves [message #59666 is a reply to message #50796 ] Sat, 05 January 2013 15:12 UTC Go to previous messageGo to next message
avatar ttoinou  is currently offline ttoinou
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I like theses fractals so I made myself one :
www.shapeways.com/model/857223/developing-koch-snowflake-fra ctal-with-holes.html
http://images1.sw-cdn.net/model/picture/674x501_857223_788501_1359658039.jpg
.
Thank you for the idea I stole anyway Razz .

[Updated on: Thu, 18 April 2013 14:54 UTC]

Re: Developing fractal curves [message #59695 is a reply to message #59666 ] Sun, 06 January 2013 00:11 UTC Go to previous messageGo to next message
avatar henryseg  is currently offline henryseg
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Very cool ttoinou!

As I said in the original post, I also stole the idea from Geoffrey Irving Smile

We wrote a paper together on these things: Developing Fractal Curves. Geoffrey has a different way to generate the surfaces, which looks like it might be similar to yours. He also did the Koch snowflake, there are some renders of it in the paper.
Re: Developing fractal curves [message #59711 is a reply to message #59695 ] Sun, 06 January 2013 10:58 UTC Go to previous messageGo to next message
avatar ttoinou  is currently offline ttoinou
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Thank you for the paper.
We both use polynomial curves but I don't know if it is the same algorithm..
And you manage to create thickness (I have to use Blender) AND it gets thinner as the iteration (or z space parameter) increase.
Doing that would be my next step Razz .

New version :
<a href=" http://www.shapeways.com/model/857320/developing-koch-square -fractal-with-holes.html" target="_blank"></a>
http://images1.sw-cdn.net/model/picture/674x501_857320_788508_1359658128.jpg

How many triangles do you have ?

[Updated on: Fri, 01 February 2013 15:28 UTC]

Re: Developing fractal curves [message #59734 is a reply to message #59711 ] Sun, 06 January 2013 21:46 UTC Go to previous messageGo to next message
avatar henryseg  is currently offline henryseg
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Hi ttoinou,

The details about how we thicken things up are in the paper, but there are lots of ways you can do it.

I made my version with NURBS surfaces, so it can be however many polygons you like. I tend to get near to Shapeways' million polygon limit if I've got a complicated model like this. Geoffrey's version of these uses meshes the whole time, and gets finer detail meshes using something called Loop subdivision, and so he can get arbitrarily detailed meshes as well.
Re: Developing fractal curves [message #59778 is a reply to message #59734 ] Mon, 07 January 2013 16:37 UTC Go to previous message
avatar CristobalGordo  is currently offline CristobalGordo
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Really cool looking things. Seems like they would maybe make good heatsinks (made out of aluminum or copper.)

 
   
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