A Different Universe: Reinventing Physics From the Bottom Down by Robert B. Laughlin

Author:Robert B. Laughlin [Laughlin, Robert B.]
Language: eng
Format: epub
Publisher: Basic Books
Published: 0101-01-01T00:00:00+00:00

It becomes easy to imagine that lifelike patterns might emerge.

A simple example of such a model is the mountain range fractal.3 A computerized map grid is refined again and again, each time assigning a fictitious height to the new grid point that is the average of the heights of the adjacent old ones plus a random increment that becomes smaller and smaller as the refinement proceeds. The heights thus generated simulate the appearance of real mountain ranges so effectively that they are often used in movies to generate backdrops, as are their close relatives the fractal cloud, the fractal coastline, and the fractal vegetable (broccoli). The physical process being emulated by the mountain fractal is presumably aggregation, a process of surface growth by which an atom diffusing in from above sticks to the first place it hits, thus encouraging large structures to grow at the expense of small ones by shadowing them out. The large literature on diffusion-limited aggregation includes beautiful computer-generated patterns resembling the leafy ice crystals that sometimes form on windowpanes in winter.4

Another complexity model—legendary on account of being one of the first discovered—is John Conway’s Life, a cellular automaton originally popularized by Martin Gardner’s “Mathematical Games” column in Scientific American.5 Life consists of a checkerboard with tokens that are removed from the board (death) or added to the board (birth) at each tick of an imaginary clock according to the following two rules:1. A token dies unless two or three of its eight neighboring sites are occupied by other tokens.

2. A token is born on an empty site if exactly three of the eight neighboring sites are occupied by other tokens.

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