Marble fractal lines and foliation

[l.k.h.heah (Lawson)]

Hi,

I was wondering if anyone could help point me in the right direction for generating fractal lines and foliation in Marble as line work. Essentially the impurities in marble creates its pattern, and I would like to generate this in Grasshopper rather than tracing an existing. I’ve started with Fields and then with land contours but it doesnt get that “blocky” feel to it.

See inspiration pics

[PeterFotiadis (Pfotiad0)]

@l.k.h.heah

fractal lines

Fractals is not the way to do that. Controlled recursion [kinda a “special” kind of swarms, so to speak] is. That said speed is the paramount issue … most examples that I’ve seen are slower than any Harley Davidson. I have some “similar” defs (I bet that Tom J has as well [swarms]) but they are carried over 100% via C# code. Notify if you want one for playing around.

But if I was you … I would do it the good old way: trace a real thing and forget computers.

[PeterFotiadis (Pfotiad0)]

Forgot to mention one of the dominent theories on fluid dynamics:

Google: C# Navier-Stokes, Navier-Stokes fluid simulation etc etc

See this classic as well:

fluid-dynamics-GDC03.pdf (1.0 MB)

[laurent_delrieu]

Did you look at procedural texture ?
There are some example, it could be simple to extract lines with color variation.
http://www.upvector.com/?section=Tutorials&subsection=Intro%20to%20Procedural%20Textures
http://lodev.org/cgtutor/randomnoise.html
A simple solution, you will need

4D Noise

marble turbulence noise.gh (15.3 KB)

[laurent_delrieu]

Just playing
{pt.x, pt.y,(1+sin((pt.x+att*noise/2)a)cos((pt.yattnoise/2)*a))/2}

[l.k.h.heah (Lawson)]

Thank you guys for the responses,

I ended up just line tracing it on Illustrator and importing the lines into Rhino… sorta cheating, but I don’t really have the time to delve into the complex maths and scripting

[laurent_delrieu]

There is no complex in the script I published. Just sliders in order to duplicate classical marble texture.
Nevertheless it was an interesting question

[grbl9789 (greg.obj)]

Hi Laurent, huge fan of your work you have posted on GH forums. Is there a way to apply this technique to a sphere instead of a rectangle? Only interested in constructing a mesh for rendering, not extracting contours.

[laurent_delrieu]

Yes it is possible to apply this technique to sphere.

Bust instead of applying contour I apply Mesh Iso Splitting, so you need to put a value (double not point) at each vertex of the mesh then iso-splitting then colorize.

Dual color model design

Hello here is a solution using Grasshopper. As I understand you want to apply displacement and depending of the displacement colorize your mesh. I have done a mesh isoplitting which could be useful. I propose you a script that is doing a real egg shape as a surface. This surface is remeshed and some displament is added as a proportion on the height with a sinus. But you could imagine whatever function you want. and then iso splitting, enter a mesh, a value for each point and an iso value and…

Relaxing Lines on a mesh

I didn’t keep the script I wrote for the example. You can recreate if you need Geodesic is there: I followed this publication but didn’t implement the simplification. So it is too long for “big mesh”. Mesh iso splitting here

[laurent_delrieu]

Here an example with no cut on the sphere.
I use a icosaedron sphere of my own. You have to specify the maximum number of vertices. Here less than half a million. I put many choices. All the equations are in C# to go faster.
Sphere is radius 1, so as noise is scale dependant. I advise you to use 1 unit objects, but it is not mandatory. You can lower the number of vertices to go faster.
Hope it helps.

marble turbulence noise on sphere no cut.gh (24.6 KB)

[grbl9789 (greg.obj)]

Thanks so much! You have been extremely helpful.

[laurent_delrieu]

[markz]

That is a great effect, Laurent

[lachlancali44]

Hi Laurent,
I was just wondering if you knew a way in which the pattern can become more sparse the further it gets from an attractor curve? I tried to play with the script you supplied, but I just cant seem to work it out.

Thanks

[felipegutierrezduque (Felipe Gutiérrez)]

We the graphics guys do this usually with a technique called Domain Warping which is similar to Laurent’s answer just warp your noise function in a noise function instead of using trig: double myNoiseValue = noise( myPosition + noise( myPosition ) ); noise here should probably be instead a fractional Brownian motion/fractal sum but a simple noise will do and is faster.

[user2669]

Hello Laurent,
I was wondering, how did you flatten the texture in grasshoper?

[laurent_delrieu]

Hello
I use a square plane mesh, then screen copy. It is also possible to generate the the bitmap withing Grasshopper.

And if you want tileable use a torus for XYZ then use UV coordinate to have to texture on a plane. There are some explanation on the forum.

See thes links

From procedural texture to image texture (How To)

Here is a way to transform procedural texture to a texture file. In this description a procedural texture is a function that transform a coordinate in euclidean space (X, Y, Z) to a colors (Red, Green, Blue and why not Alpha). Unwrap the object(s) you want to texture, this object could be also an object that is just used as support of UV mapping (used with Texture Matching) [image] 1bis) You can edit the UV map in UV editor in order to optimize the placement of objects. [image] Extract…

Periodic noise? 4d noise, tundra

If it is on 2d it is possible. You have to apply 3d noise on a torus and then use uv of the torus as XY. It is not very uniform so you will have to play with GraphMapper size, the torus parameters … [image] [image] You’ll need Lunchbox for the Torus periodic noise.gh (13.9 KB)

[felipegutierrezduque (Felipe Gutiérrez)]

Note getting periodic noise is really easy once you get the gist of it, the trick is simple: mod your coordinates, is that easy. So you take your UVs and simply do % with the size of the texture, it doesn’t work for everything but for most “classic” noise generation techniques like Perlin, Value, etc… it is that easy. There are examples for that online search for tileable perlin or whatever shader and there probably exists a shadertoy that does it.

[Diego_Eslava]

Hello Laurent, I admire your work, but, I have tried to transform procedural texture to a texture file, with this file of yours, but I cannot convert it into an image, could you please explain how you do it a little clearer with an image of the file gh. I appreciate your help

[laurent_delrieu]

Hello
as it is described in this post there are many ways.

As now there are also many image plugins, from JAVID,
Build Bitmap

Javid

IMAGE
Build Bitmap

Bitmap +

Here a way using the excellent Nautilus plugin

Nautilus

Take a Mesh Plane (Bitmap will be (number of face+1)*(number of face+1))
Take a component that put colors on a Mesh (here Fast Noise Lite from Nautilus)
Plug a Gradient if you want something different than black and white
Use Object to Image that try to convert a rectangular mesh to an image, it converts also a File Path or an image !
Then export using Save Bitmap from BITMAP+ plugin

And now if you want tileable texture, use a torus Twisted Torus, for example

colored mesh to tileable bitmap.gh (19.6 KB)
colored mesh to bitmap.gh (16.0 KB)

Related to this discussion

Nautilus plugin

@Mahdiyar thanks for the interests and suggestions. I have now changed a bit the way inputs and outputs work. For the input of 3 component they accept as image A path An image A mesh (if mesh is similar in topology to a Mesh Plane So the fun thing for example is take a Twisted Torus and apply Reaction Diffusion Extended Reaction Belousov or Noise on Mesh then send the colored mesh to a tool that transform a FilePath, an Image or a Mesh to an Image, a Mesh, The rectangle cell and Width and Hei…

For tileable I think an extra pixel row and column could help. It is the main problem of conversion between mesh and image. Most of the time color is on vertex but for image color is on pixel (face for a quad mesh). So you could use