IN THE MIND’S EYE, a fractal is a way of seeing infinity.

Everything we care about lies somewhere in the middle, where pattern and randomness interlace.

In a way, art is a theory about the way the world looks to human beings. It’s abundantly obvious that one doesn’t know the world around us in detail

We have met the Devil of Information Overload and his impish underlings, the computer virus, the busy signal, the dead link, and the PowerPoint presentation.

it struck me as an operational way to define free will, in a way that allowed you to reconcile free will with determinism. The system is deterministic, but you can’t say what it’s going to...

Vengeful conquerors burn books as if the enemy’s souls reside there, too.

The only things that can ever be universal, in a sense, are scaling things.

Thinking about language, while thinking _in_ language, leads to puzzles and paradoxes.

the brain does not own any direct copies of stuff in the world. There is no library of forms and ideas against which to compare the images of perception. Information is stored in a plastic...

There are two kinds of geniuses: the ‘ordinary’ and the ‘magicians’. An ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There...

the pattern appears so ethereally, that it is hard to remember that the shape is an attractor. It is not just any trajectory of a dynamical system. It is the trajectory toward which all other...

Ideas that require people to reorganize their picture of the world provoke hostility.

Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world.

You don’t see something until you have the right metaphor to let you perceive it

The early sense of self-similarity as an organizing principle came from the limitations on the human experience of scale.

One simple but powerful consequence of the fractal geometry of surfaces is that surfaces in contact do not touch everywhere. The bumpiness at all scales prevents that. Even in rock under enormous pressure, at some...

The fractal structure nature has devised works so efficiently that, in most tissue, no cell is ever more than three or four cells away from a blood vessel. Yet the vessels and blood take up...

Billions of years ago there were just blobs of protoplasm; now billions of years later here we are. So information has been created and stored in our structure. In the development of one person’s mind...

Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern.

The boundary is where points are slowest to escape the pull of the set. It is as if they are balanced between competing attractors, one at zero and the other, in effect, ringing the set...

The pits and tangles are more than blemishes distorting the classic shapes of Euclidian geometry. They are often the keys to the essence of a thing

superintelligent,” but compared to a real organism it is an idiot savant. Not only do living things lessen the disorder in their environments; they are in themselves, their skeletons and their flesh, vesicles and membranes,...

Of all the possible pathways of disorder, nature favors just a few.