Do gluons decay? I have seen examples of other particles that decay into gluons but do gluons themselves ever decay. Since gluons are not composed of anything else I assume they are fundamental.  
On there other hand some fundamental particles decay and some do not i.e the photon.  But on the other other hand some non fundamental particles do not decay either. i.e proton.
Maybe I am getting tangled up in semantics.  Instead of decay would transformation be a better description.  
 A: In the standard model of particle physics  zero mass elementary particles, of which the gluon is one if you look at the table, cannot decay. This is because the standard model is formulated on fourvectors of special relativity, and has to obey basic quantum mechanical conservation laws, as energy and momentum conservation. 
If a zero mass particle were to decay within this framework, the decay products (as an example two particles) would have as an invariant mass, the length of the added four vectors, . This  would contradict energy and momentum conservation , as the before (gluon four vector ) and after decay(summed four vector  of the two decay products) four vectors should be the same .
The gluon plays the same  role as the photon for the strong interactions.
A: A gluon does not decay in a standard sense. There are a number of reasons, but the simplest is to consider the decay of any massless particle. The energy-momentum vector for a massless particle is $(E,~\vec pc)$ which with $E~=~\hbar\omega$ means
$$
P^\mu~=~\hbar\left(\omega,~\omega~\hat n\right).
$$
Here $\hat n$ is a unit vector along the motion of the massless particle. Since the photon is massless $P^\mu P_\mu~=~$ $E^2~-(pc)^2~=$ $\omega^2~-~\omega^2~=~0$. This is an invariant, so what ever decay happens it must be the case this is upheld. It is clear the massless particle can't decay into massive particles for such particles obey $P^\mu P_\mu~=~(mc^2)^2$. Clearly this massless particle can't decay into two massless particles that have momenta in different directions.
Let us consider a gluon that transforms into two gluons. A gluon is a state $g^{cc'}$, where the color indices $c$ and $c'$ define the QCD state of the gluon. Now suppose we have $g^{cc'}~\rightarrow~g^{cc"}~+~g^{c\bar c"}$. Here the color indices $c"$ and $\bar c"$ correspond to a color and its opposite. We then have the requirement the frequency of the original gluon is conserved with $\nu~=~\nu_1~+~\nu_2$. In effect this is a QCD version of the parametric down shift of a photon in quantum optics. I am not sure how this can occur in QCD, or if it has been considered. I see nothing impossible about this. 
A: Yes, gluons eventually do decay by the factor:
GluonDecayFactor[q_, s_, l_] :=
q^6*$d^{\mathcal{L}}$*h[\mathcal{L}] G[s, q, \mathcal{L}] S[$d~\mathcal{L}~s$, q $\mathcal{L}$, 4].
h[\mathcal{L}_]^2 -> [Zeta]2 /; \mathcal{L} > 0
Using a coordinate system similar to:      Axiom 1: \begin{aligned}
F[q,s,l,[Alpha]] &= \frac{\sqrt{-q^2+2 q s-s^2+l^2 [Alpha]^2}}{[Alpha]}\\\\
G[q,s,l,[Beta],c] &= \frac{\sqrt{-c^2 (l [Alpha])^2+c^2 q^2-2 c^2 s q+c^2 s^2+c^2 (l [Alpha])^2 \sin^2{[Beta]}}}{\sqrt{-1. (l [Alpha])^2+q^2-2. s q+s^2+(l [Alpha])^2 \sin^2{[Beta]}}}
\end{aligned}
