Paradigm Shifts

Yet Pollock's reputation has outlived his detractors. Others said that a trained chimpanzee could do just as well. )In 1949, when Life magazine asked if Jackson Pollock was "the greatest living painter in the United States," the resulting outcry voiced nearly half a century of popular frustration with abstract art. Respectively, these three things mean that it is unpredictable, at the same time regular, and indecomposable. This tiny insect sneezes, halfway around the world from the reader.

While these scientific definitions may be great to give a scientific definition of chaos theory, they do little to really explain what it is. In other words, the function moves around seemingly randomly without ever settling into a fixed pattern. In short, the two definitions overlap quite a bit, but aren't synonymous by any definition. However, few people know in any real detail what chaos theory entails.

Another definition defines chaos as a trajectory that is exponentially unstable and neither periodic nor asymptotically periodic. While this specific chain of events is highly improbable and implausible, it does illustrate the point well - a chaotic system is one that is very sensitive to initial conditions (something as small as a butterfly sneeze can cause something as large as a hurricane).

One scientific definition of chaos calls a function or system chaotic if it is extremely sensitive to initial conditions, periodic points are dense, and it is topologically transitive.

Fractals may seem haphazard at first glance, yet each one is composed of a single geometric pattern repeated thousands of times at different magnifications, like Russian dolls nested within one another. That logic, says physicist and art historian Richard Taylor, lies not in art but in mathematics—specifically, in chaos theory and its offspring, fractal geometry. ) Then he scanned the photographs into a computer and divided the images into an electronic mesh of small boxes.