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I mostly have cave crystals that grow on their own on my mind, along with perhaps river channels that change their shape over time - but perhaps there are some other, better examples. Also, the more examples, the better.

  • There is spontaneous radioactive decay. This is perhaps more "spontaneous" than the crystals growing since it is not potentially deterministic, but the "decay" suggests it is not increasing complexity, however, that might not be the best way to describe the resulting products after the decay. I don't really know a good answer, but I hope others have one. Welcome to this SE! – Frank Hubeny Oct 25 '18 at 12:31
  • You can go from a solid chunk of some radioactive isotope or other into a chunk of varied elements, which looks to me like becoming more complex. – David Thornley Oct 25 '18 at 17:12
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There are many self-organizing, non-living complex systems. The weather is one (with the Great Red Spot on Jupiter perhaps representing its pinnacle as a self-organizing system). Snowflakes are another, and the shapes of rivers are a third.

If you are interested in this topic, then I highly recommend that you research chaos theory. James Glieck's Chaos is the canonical beginner's introductory text.

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The best example is probably our universe! Current models of mass and gravity, plus some chemistry, show that the galaxies and stars that we see have "evolved" from previous forms and become quite complex indeed. See this Youtube user page for a variety of animations.

https://www.youtube.com/watch?v=6L1N95IRG8I

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