Has there been any attempts to create time-independent model of physical world?
It depends what you mean with model. I'd say to a certain extent the "standard view" of physical law is timeless, and time (t) only emerges when you choose an observer. But the laws of physics and the symmetries of physics are according to standard reasoning timless or eternal, since the laws of physics are often assumed to obviously be observer independent.
OTOH, if you want to hear some brief objections to this more common view, see Smolins philosophical talk http://pirsa.org/08100049
No - what I was thinking that maybe time itself could be some fundamentals interacting.
Of physical word - no, but there are time-independent phenomena, called usually static ones.
There are also physical variable combinations independent of time. The most known are the total energy, momentum, and the angular momentum. These are additive in particles. There are also many others but they are not additive in particles. In terms of them there is no time because their values are conserved.
Euclidean shape from motion:
Could we reverse this and have motion from Euclidean shape?
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