How does time plus matter plus chance produce logic and rational?

How is it that science which is based on physics, chemistry, biology, and mathematics, which are all based on logic, rational thought, and repeatable experiment proposed by a thinking and purposeful mind, come to be evolved out of mere atoms from rocks such as Carbon, Hidrogen, and Nitrogen, and time and random chance? Since chance is random and chaotic by definition would it evolve a life that is so uniform and a thought process that is so logical? If life truly evolved from chaos, would it not be more logical for everything in our world to be more illogical and none-repeatable? Would it not be more logical for everything in our universe to have no similarities since each item and event would be singularly based upon random chance? In other words, would such a chaotic world produce the symmetry of the honeycomb or the beauty of a Pea's tail? Should science, which is based on logic and repeatable experiments to prove a theory even exist? In a world of chaos and chance, science as we know it, which is based upon rational and logical thought processes, should not exist, would it? Life as we know, with so much order and similarity, should not exist, would it? Can anyone explain, and if so is that explanation a chance explanation or random explanation, or is it based upon a rational and logical thought process?