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One consequence is a dramatic broadening of the domain to which computational ideas can be applied—in particular to include all sorts of fundamental questions about nature and about mathematics.
Yet what the discoveries in this book now show is that there are all sorts of systems that have much simpler structures, but that can nevertheless perform very sophisticated tasks.
Then after an initial period where the models are often said to be too simplistic to be worth considering, there begin to be all sorts of extensions added that attempt to capture more effects and more details.
At first there is then rapid expansion, with many new species trying out all sorts of possibilities that have been opened up.
And what makes this possible is that even though individual cells follow the same rule, different configurations of cells with different sequences of colors can together produce all sorts of different kinds of behavior.
But it turns out that this very same angle also shows up in all sorts of other features of plants, as shown in the pictures at the top of the facing page .
One can imagine all sorts of schemes by which such colors could be updated.
For with calculus there was finally real success in taking abstract rules created by human thought and using them to reproduce all sorts of phenomena in the natural world.
For it is what allows us to characterize all sorts of physical systems by just specifying a few parameters such as temperature and chemical composition—and avoids us always having to know the details of the initial conditions and history of each system.
And in fact, as I mentioned at the end of the previous section , what I expect instead is that there will always tend to be all sorts of complicated and seemingly random behavior at small scales—though at larger scales this will typically get washed out to yield the kind of consistent average properties that we ordinarily associate with space.