Embedding information in random bit sequences while maintaining certified randomness

[bsr]

Anybody else ever get an errno 28 (no space left on device) when trying to post?  I made a custom SIRDS for the list but if I attach it I always get errno 28.  Oh well...

On 8/31/21 12:46 AM, Jim Cheetham wrote:
> I don't know where he got it from either, but there's an image on Wikimedia
> that looks extremely similar ...
> https://commons.wikimedia.org/wiki/File:Stereogramme_PI.jpg.
>

Nice find.  That is it.  Going down the rabbit hole just a little, there is a lot of information.  Technically it is a SIRDS (Single Image Random Dot Stereogram) better known as "Magic Eye".

> Sadly I don't think I have the maths to describe why something that
> obviously has structure (e.g. that stereogram) is potentially passing the
> tests.

Me neither, but here is an excellent place to start:

https://www.ime.usp.br/~otuyama/stereogram/basic/index.html

src code:
https://www.ime.usp.br/~otuyama/stereogram/gallery/sirds/


I found the following statement fascinating and it may explain passing randomness tests.  However, it dates from 2006, so I wonder if our understanding has changed any.

"The random dot stereogram is a scientific proof. It has an axioma: random dots do not convey any kind of three dimensional information (shape from shading, contours, etc). If you present only one image, you cant say what is the hidden image (it is only random dots, see axiom). So neurons at retina are not responsible for the stereopsis. But when you see both images, you can say what is the hidden image - stereopsis occur somewhere in the brain. You can say more: somewhere in the brain that receives information from both eyes."    (quoted from here  -  https://en.wikipedia.org/wiki/Talk:Random_dot_stereogram )