There are no patterns. When a particle decays, the moment when it does so is absolutely random, chosen from the distribution
$$ P_{\rm decay}(t\lt T\lt t+dt) = \frac{dt}{t_0}\cdot \exp(-t/t_0) $$
For $t=t_0$, the beginning of time when we knew that the particle still existed, the exponential is equal to one and we see that the "probability of the decay per unit time" is $1/t_0$. As the probability that the particle still exists exponentially decreases, so does the probability that it decays at a later moment.
The randomness of the decay time is just another example of the randomness that quantum mechanics, the basic framework for all the laws of physics since 1925, predicts for every phenomenon in Nature.
In the most widespread description of quantum mechanics, the decaying particle is described by a wave function. And that wave function evolves into a superposition of the undecayed and (various) decayed components, and the probability amplitude (value of the wave function) associated with the undecayed particle decreases as $\exp(-t/2t_0)$. This probability amplitude has to be squared and the result, $\exp(-t/t_0)$, gives us the probability that the particle hasn't decayed yet.
Theories that would try to find some "internal" reason why the particle decayed at the given moment are called "hidden variable theories" and they may be shown incorrect – either incompatible with the experiments about the decay in this case, or with experiments backing the special theory of relativity. So physicists have to embrace the intrinsic randomness of Nature as a fact. The randomness of the decay time is a Nature's perfect random generator, one that can't be fooled or cheated.
