meaning…

There were mathematicians, physicists, biologists, chemists all making connections between different kinds of irregularity. Physiologists found a surprising order in the chaos that develops in the human heart, the prime cause of sudden, unexplained death. Ecologists explored the rise and fall of gypsy moth populations. Economists dug out old stock price data and tried a new kind of analysis. The insights tat emerged led directly into the natural world – the shapes of clouds, the paths of lightning, the microscopic intertwining of blood vessels, the galactic clustering of stars.

chaos… 

In the context of that debate, chaos brought an astonishing message: simple deterministic models could produce what looked like random behavior. The Behavior actually had an exquisite fine structure, yet any piece of it seemed indistinguishable from noise. The discovery cut though the heart of controversy.

measuring the coastline…

An observer trying to estimate the length of England’s coastline from the satellite will make a smaller guess than an observer trying to talk its coves and beaches, who will make a smaller guess in turn than a snail negotiating every pebble. Common sense suggest that, although these estimates will continue to get larger, they will approach some particular final value, the true length of the coastline. The measurement coverage, in other words. And in fact, if a coastline were some Euclidean Shape such as a circle, this method of summing finer and finer straight line distances would indeed converge. But Mandelbrot found that as the scale of measurement becomes smaller , the measure length of the coastline rises without any limit, bays and peninsulas revealing even smaller subbays and subpeninsulas – at least down to the atomic scales where the process does finally come to an end . Perhaps.