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https://youtu.be/VVvaVvRViYQ

Hi Darkbeam,

 if we could print a normal sized 3D fractal down to the nanometre resolution, then an interesting effect is that it would get colour.
While things often get colour from their pigments, other things such as opals, butterfly wings, certain metals, get their colour from their shape at roughly the nanometre scale. So called structural colouring http://www.fractalforums.com/new-theories-and-research/real-colour-fractals/msg13616 (http://www.fractalforums.com/new-theories-and-research/real-colour-fractals/msg13616).

It seems to me, that on average, fractals would have a tan or reddish tinge, as the geometry is bigger at the bigger scales (i.e. larger wavelengths, such as red), this is apparently the reason why copper has its colour. But beyond that, I imagine the colour would vary with the fractal and with the chosen base size. Highly ordered fractals like the Menger sponge may have iridescence (like opals), and more disordered / complex shapes like the mandelbox might be more pastelly (many different wavelengths reflected).

The technology in this video  was so cool that I MADE my nephews  watch it :police:

Here's my attempt at structural colouring of a 1cm wide scale -1.5 mandelbox:
(https://2.bp.blogspot.com/-0W8gh2PFBxQ/WFyBftkbsII/AAAAAAAAA8A/l1qCQAkgbaEU2eHMOjubtmYZEY-ym_i3wCLcB/s400/rgb1cm5x5-2.png)
full image (https://2.bp.blogspot.com/-0W8gh2PFBxQ/WFyBftkbsII/AAAAAAAAA8A/l1qCQAkgbaEU2eHMOjubtmYZEY-ym_i3wCLcB/s1600/rgb1cm5x5-2.png)
It is subtle as most of the box faces are quite flat, but you can see that the edge of the flat areas goes a bit brown and the tiny encrusted cubes have a blue tint.
I am not at all certain that this is the correct structural colour as the physics is pretty daunting. But the idea is that red light (wavelength 450nm) will interact with the fractal like it is smooth at scales 450nm, whereas blue light will interact with the fractal like it is smooth at 650nm. So I just render the fractal 3 times, once for red, green and blue, and change the minimum distance (minDist) to be 450nm, 550nm and 650nm respectively. fragmentarium script attached (make sure your iteration counts are up high).  

and here is the mandelbulb:
(https://4.bp.blogspot.com/-9h6GpZjp5pU/WFyHQD7s7uI/AAAAAAAAA8k/eHZvc6bYQ_kad7PYQRMFt1tljKwzD6MZACLcB/s400/mandelbulb-2.png)
full image (https://4.bp.blogspot.com/-9h6GpZjp5pU/WFyHQD7s7uI/AAAAAAAAA8k/eHZvc6bYQ_kad7PYQRMFt1tljKwzD6MZACLcB/s1600/mandelbulb-2.png)

some more details are in my blog: http://tglad.blogspot.com.au/2016/12/the-colour-of-3d-fractals.html (http://tglad.blogspot.com.au/2016/12/the-colour-of-3d-fractals.html)

Interestingly, some very recent papers are starting to look at the colour of fractals:
https://arxiv.org/pdf/1507.07376.pdf (https://arxiv.org/pdf/1507.07376.pdf)
in this one they get a colour spectrum for a Cantor cluster, in fig 8a... horizontal axis proportional to light frequency. Am I right to interpret this as a brownish colour for the fractal? (assuming visible light to lie in the middle region)... i.e. more intensity in the lower frequency colours.

I was about to ask it to you thanks :D

Wow, this nanoscale 3D printing is not just a lab experiment, it is commercial https://3dprint.com/122337/nanoscribe-microscale-printing/ (https://3dprint.com/122337/nanoscribe-microscale-printing/)... so if they offered a printing service (rather than selling the equipment) we could send them a 3D fractal and see what it looks like.

It is right on the borderline of being useful... its resolution is 400nm horizontal and 1000nm vertical (450nm is the wavelength of blue light). The problem is that it can only print something 1/3 mm tall at this resolution (though the images show stuff over a mm). So almost enough to see what it would look like.  (note that details much smaller than 400nm have almost no effect on the result).

but not quite... maybe in a year or two it will be possible to print a few and see.

I've found out that a nanoscale fractal has already been built!:
(http://jrgreer.caltech.edu/content/home/fractal_nanotruss.jpg)
http://www.caltech.edu/news/miniature-truss-work-42850 (http://www.caltech.edu/news/miniature-truss-work-42850)
The structure width seems to be about 500nm, around the wavelength of blue or green light.

I e-mailed the head of this project and she confirmed that the shape has colour due to its shape, or opalescence (which I assume is like iridescence), so visually it has what are probably blue/green colours that vary with viewing angle, like oil film or peacock feathers.

It is nice to know this structural coloration really happens in practice.

Fractal structure!!!! Yaay :) nice

that truss is awesome. I wonder what it would look like if you stacked copies of them together to an appreciable scale.

And here she is, talking about light-weight, high-strength nano structures:

https://www.youtube.com/watch?v=Dahz8wYWvos