Word for a decaying and renewing system, like a coral reef
Solution 1:
What about "organic" - that's sometimes used to describe eg. cities that have the quality you describe.
So, somewhere like "Canberra" is not organic - it was built all of a piece at one time. You could say the same about Paris, Napoleon built it all at once in the one style.
But Tokyo or something is a crazy "organic" city, an amalgamation built over various periods all jumbled together.
Solution 2:
If a city was designed from a clean sheet, then use designed. If the city began as a small village and later evolved into a city, then use evolved.
Note this is specific to a system that can be designed rather than an organic system.
Solution 3:
A word that's missing from this conversation so far:
Regenerative: tending to or characterized by regeneration.
Source.
Regenerative does not convey the 'patchwork' aspect which you rightly used to describe natural habitats like coral reefs, but I see no reason you couldn't describe such a habitat as a 'regenerative patchwork'.