Looking For The Equilateral Triangle

Is order a question of perspective? Is there such a thing as randomness, or is what we perceive as a random event just the fragment of a pattern or a sequence too large in space and time for us to perceive?

This investigation focuses on the seemingly unpredictable nature of events that we call chance. Are these random coordinates really independent from one another or is there a connection that could reveal a plan that is progressing the work towards a clear pattern?