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My kids are older now, and I can't remember specific titles, but I would search for books about Fibonacci; I think we found several good ones. There was a math section in the children's library that had several books like this. You might also search for things on fractals, even snowflake books might have some of what he's interested in.
He might also enjoy Vi Hart's YouTube videos, I know there is one on Fibonacci, but many are about patterns (maybe not so much about nature, though).
Basically had the same thoughts as cricket3, no specific book reference.
For hands on work, the Fibonacci sequence can be seen by counting the petals in each ring of a flower. I think corn kernel rows on a cob also are good for it. The Golden Ratio/Golden Number/Phi is also a fun discoverable number as it is rooted in the Fibonacci sequence, and it shows up in many places in nature (such as the human head width to height ratio.)
When my kid was 6 and interested in patterns in nature, these were some of the Fibonacci resources that were a hit:
Books:
- Blockhead: The Life of Fibonacci (Joseph D'Agnese). A compelling biography. - Growing patterns: Fibonacci numbers in nature (Sarah C. Campbell). Cool photos.