A friend of mine pointed me to this description on how to make
fractal cookies. They're beautiful and no doubt amazingly delicious. They in turn link to a description of
fractal pizza, which looks less delicious but is perhaps conceptually more interesting:
The idea was simple, as are most truly genius moments. When looking at a pizza I noticed that you had bread, sauce, cheese and toppings. The toppings struck me as interesting. No matter what you put on top of the bread, sauce, and cheese you still had pizza. Initially I had the same thoughts of the many pizza innovators that have gone before me, 'What is the craziest thing I could put on pizza!??'
It was my love of the term "meta" that turned me on to the idea. What is the craziest thing to put on pizza? Well, what about more pizza!??! I almost dismissed the idea initially, as I have eaten pizza with two crusts, and even stacked slices on top of each other... but I couldn't let go of the idea of a meta-pizza and then while wandering the frozen food aisle of my local grocery store it was like Newton's apple hit me on the head and said, "The pizza comes in a wide variety of sizes." Eureka!
The idea is called "self similarity". With pizzas of infinitely many sizes, any time you zoom in on a pizza you still see a full pizza topped with mini-pizzas! Deliciously brilliant I must say.
This inspired me to post an idea I had the other day: fractal symbioses. I know real ecosystems have fractal properties. That's not the point. In my fractal ecosystem, which I'll call fractal rock, you start with a medium-sized animal like a tiger. Then you take an animal that is about the size of that animal's prey but which (1) is a scaled down copy of the original animal (e.g. a housecat), and (2) is a symbiote. Maybe the housecat rids the area of mice and other vermon that the tiger doesn't want to bother with.
But that's only one layer of self-similarity. There needs to be a smaller cat, as small to the housecat as the housecat is to the tiger. And then there needs to be a bigger cat!. I think four generations is enough to get a really cool fractal symbioses going. We can potentially go smaller with cats the size of shrews. But any bigger and we'd be on dinosaur scales, and that's just scary.
