Proof of universality of Game of Life is straightforward (CAFAQ):
(two annihilating glider streams with gaps (ie. 0s) are colliding, one is "data" and the second is all glider filled, ie.: 111111...) For every 0 in the input byte, the missing glider in the input stream allows a glider from the glider gun to pass, whereas for every 1 in the input byte, a glider in the input stream annihilates the corresponding glider coming from the glider gun. Thus, looking at the output stream from the glider-gun DOWNSTREAM of the collision site, there is a glider (a 1) for every "hole" in the input stream (a 0) and there is a hole (a 0) for every glider (1) in the input stream. Thus, the filtered output of the glider-gun is the logical NOT of the encoded input stream.
And not a universal computer in sight!
By colliding this output stream (call it NOT A if the input steam is A) with another input stream, B, one gets A AND B in the continuation of the input stream B after the collision site.
So what is sufficient for universality is a particle $\alpha$ such that after collision with itself complete annihilation occurs $\alpha + \alpha = 0$. This seems to be an easy requirement. However, ECA 110 (or Rule 110) was proved via simulating cyclic tag system. And ECA 54 was not yet proven to be universal.
Both ECA 110 and ECA 54 have rich glider/particle sets. I did not yet dig deep into the glider sets. I first want to ask:
Was the contrast between simplicity of $\alpha + \alpha = 0$ and problems with proving universality of ECA examined somehow? Are the particle systems categorized in some way, to explain why rich particle systems are not necessary universal, while system as simple as $\alpha + \alpha = 0$ can be universal?
