Tag: chaos, geometry

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

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

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

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 sufficiently small scale it becomes clear that gaps remain, allowing fluid to flow.

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 little space, no more than about five percent of the body.

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

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 trajectories converge.

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

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 at a distance of infinity.

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 from childhood, information is clearly not just accumulated but also generated—created from connections that were not there before

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 way, allowing fantastic juxtapositions and leaps of imagination. Some chaos exists out there, and the brain seems to have more flexibility than classical physics in finding the order in it.

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