You're forgetting living systems. We certainly exhibit CSI by any reasonable definition, and we know for certain where we come from. (Our parents.) So in all known cases, CSI is produced by either an intelligent agency or reproduction. Then there are complicated weather patterns, interlocking geyser systems, natural nuclear reactors, sand spits, etc. etc. that exhibit some CSI, which aren't known to be produced by either intelligence nor reproduction with mutations. <shrug>
What about natural nuclear reactors exhibit CSI? Or what level of CSI? Certainly nuclear fission is a complex phenomena, but what would be the independently given pattern that would make specified?
Deep under African soil, about 1.7 billion years ago, natural conditions prompted underground nuclear reactions. Scientists from around the world, including American scientists have studied the rocks at Oklo. These scientists believe that water filtering down through crevices in the rock played a key role. Without water, it would have been nearly impossible for natural reactors to sustain chain reactions.
The water slowed the subatomic particles or neutrons that were cast out from the uranium so that they could hit-and split-other atoms. Without the water, the neutrons would move so fast that they would just bounce off, like skipping a rock across the water, and not produce nuclear chain reactions. When the heat from the reactions became too great, the water turned to steam and stopped slowing the neutrons. The reactions then slowed until the water cooled. Then the process could begin again.7
Scientists think these natural reactors could have functioned intermittently for a million years or more. Natural chain reactions stopped when the uranium isotopes became too sparse to keep the reactions going.
[snip]...Scientists believe that similar spontaneous nuclear reactions could not happen today because too high a proportion of the U-235 has decayed. [perhaps this is the reason that nuclear fission on earth today is the result only of intelligent agency] But nearly two billion years ago, nature not only appears to have created her first nuclear reactors, she also found a way to successfully contain the waste they produced deep underground.
Cordially,