THE WHOLE WITHIN THE PART
Because there is no focusing lens, the plate appears as a meaningless pattern of swirls. Any piece of the hologram will reconstruct the entire image.
The Holographic Paradigm & Other Paradoxes (1982)
Each thing is a miniature replica of the whole - a composition. The microcosm is in every respect like the macrocosm, according to scientists and sages.
Natural Reality & Abstract Reality (1919-1920)
To see a World in a grain of sand,
And a Heaven in a wild flower,
Hold Infinity in the palm of your hand,
And Eternity in an hour.
"Auguries of Innocence" (~1803)
SELF-SIMILARITY AND CASCADES
Until now we stressed that coastlines' geometry is complicated, but there is also a great degree of order in their structure.
Although maps drawn at different scales differ in their specific details, they have the same generic features. In a rough approximation, the small and large details of coastlines are geometrically identical except for scale.
One may think of such a shape as drawn by a sort of fireworks, with each stage creating details smaller than those of the preceding stages. However, a better term is suggested by our Lewis Richardson's noted work on turbulence: the generating mechanism may be called a cascade.
When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar.
-BENOIT B. MANDELBROT
The Fractal Geometry of Nature (1982)
Stars shine, planets are round, bridges remain geologically rather small, cells divide rapidly, atoms randomly vibrate, electrons disobey Newton, all because of scale.
-PHILIP & PHYLIS MORRISON
Powers of Ten (1982)
For who does not see that a horse falling from a height of six or eight feet will break its bones, while a dog falling from the same height ... will suffer no harm? ... A little dog might carry on its back two or three dogs of the same size, whereas I doubt if a horse could carry even one horse of the same size.
Discourses Concerning Two New Sciences (1638)