Random process can result in detectable patterns
I was asked a question, a very simple one, when one looks at the sky, one is able to see three collinear stars. Why so? Its quiet simple. Formation of stars is a random process. A star can be formed any where in this universe. Take take a hand full of pebbles, drop it on a table. Do it repeatedly. Before you reach the 1000’th drop, you can notice that three pebbles are (nearly) collinear. Its just a random event that three stars appear to be collinear when see from Earth. If you happen to see the same three stars from another star system, they may appear non collinear.
Another stunning example of random process is the existence of life on this planet. Everything has to come right for life to begin, develop, sustain and evolve into a complex being like apes and humans. Yet random process has made us what we are. Another example would be a billards table. Sometimes the white ball, the color ball and the pocket wil be in the same line. The striker can score a dead easy point(s).
So when a random thing happens many number of times, some times its produces stunning result. Some result could be even be repeated more than once. If humans are very agressive in deep space exploration, before A.D 3000, we could be communicating with intelligent life like our own. Who knows what the future holds for us?