Fractals are interesting -- I just read a story by Oliver Sacks about a boy with autism who could draw perfect replicas of the style of a building, while making mistakes about the number of smokestacks or windows for example. Styles might correspond to some sort of fractal. I do a lot of brain dissections -- the trachea that sheath the brain are obviously fractal, and as I zoom in to get a better look at different structures I see the same patterns repeated over and over. Afterward, if I close my eyes, I see similar fractals that shift -- they are not actual images of what I saw, but imaged generated based on what I saw.
Biomimicry is an interesting field -- lately I've bifurcated from thinking about biomimicry purely in physical or visual (ie the fractals you can look at) ways to thinking about it in terms of systems engineering design. There are a number of japanese design concepts that are now enshrined in American manufacturing. Muda, Poka-Yoke, "Batch and Queue" Vs. "Just in Time" (I think there are japanese words for these also but I can't find them).
I've been thinking alot about HOW science is done, what the bottlenecks are, and how that corresponds to biology. You know the standard gene-->RNA-->protein? I'm wondering how similar that manufacturing process is to the manufacturing of cars. I know mistakes are made and that error-detection systems exist in both. Interestingly, I just learned about the "go/no-go" action initiation checkpoint in the mind/brain. At some point you decide whether or not to move your arm (about 1/2 second before you actually move it, at least in some studies) and that processing step has been localized to an anatomical substrate.