Image: DANIELS & DANIELS COLORED WATER DROPLETS descending through mineral oil provide a slow-motion study of chaos. By varying the flow rate of the apparatus, the observer can witness a system's transition from predictable to chaotic.

When I was a physics student, I spent most of my time studying things that didn't exist--frictionless pulleys, massless springs, gravitational fields that don't change with height. Scientists have recognized for some time that real systems interact with their environment in ways that elude practical measurements, and over time these effects accumulate. So we've known that idealized solutions can describe systems for only so long. What we didn't realize was just how brief this time period could be.

In the 1980s researchers learned that for many real systems the myriad uncooperative complications of nature cause observations to disagree with predictions extremely quickly. You can, for example, take all the temperature, pressure and wind-speed readings you want, but you just won't have enough information to forecast the weather accurately more than seven days ahead. The reason is that the effects of tiny perturbations, even a jet flying over Salt Lake City, can build much more rapidly than scientists had realized, altering the weather in unforeseen ways. Systems that tumble rapidly into unpredictability are aptly termed "chaotic."

Now, thanks to a delightful device developed by Mahlon Kriebel, a professor of neuroscience and physiology at the SUNY Health Science Center at Syracuse, you can explore the subtleties of chaos at your own kitchen table. Kriebel's apparatus is a slow-motion version of another chaos classic¿--the dripping faucet. By dropping colored water droplets through mineral oil, Kriebel slows them enough that the onset of chaos can be readily observed and studied.

A graduated cylinder with a volume of 1,000 cubic centimeters makes an ideal chimney to hold the mineral oil, but a tall, clear flower vase would also work well. For the reservoir to hold the colored water, you can use a hot-water bottle with tubing attached. Cut the tubing and mate it with a barbed hose adapter to some Tygon tubing. You'll need a hose clamp to control the flow rate through the tubing and nozzle. Almost any hardware store should have the necessary hose adapter, clamps and tubing. To keep the hot-water bottle well above the nozzle, I fastened the bottle to the back of a chair and placed it on top of my kitchen table.

Kriebel fashions his nozzle from the tip of a pipette, but eyedroppers are easier to come by. The opening on mine was too wide, so I filled the tip with candle wax and then used a heated sewing needle to melt a tiny hole in the wax. Hold the tip of the needle against the wax with a pair of pliers and touch a hot soldering iron to the needle right near the dropper. Applying firm and steady pressure will quickly bore the needle through the wax plug. After that's done, insert your nozzle into the Tygon tubing and secure the connection with a liberal dose of aquarium cement.

Next, to keep the tubing in place after you've situated it, tie it to a length of coat hanger. Use sewing thread and not twine, because the latter sheds fibers that will contaminate the oil. Then install the assembly into the cylinder with the nozzle's exit hole centered about 10 centimeters (four inches) below the top of the cylinder.

Image:JOHNNY JOHNSON RETURN MAPS plot a series of numbers in terms of their sequence. For the first point, the x coordinate is the first number in the series and the y coordinate is the second number. For the next point, the x coordinate is the second number and the y coordinate is the third number, and so on. From left to right, the graphs are for increasing flow rates of the experiment (darker dots indicate a greater number of instances of that event). Note that as the flow rate is increased, the system becomes less predictable. At the highest rate, shown in the rightmost graph, the system has become chaotic.