THE PROCESS of generating a speech-flake begins with the waveform of a particular sound. Its jagged trace shows how the sound's amplitude or loudness changes over time. Pickover selects a segment of the waveform that lasts for half a second. Starting at one end, he records the height (corresponding to the amplitude) at 5,000 equally spaced points along the waveform. The data are then mapped into a snowflake-like pattern.

Suppose the first sampled point has an amplitude of 40 (on a scale from 0 to 50), the second an amplitude of 30, the third 35, the fourth 25, and so on. These values are plotted on a graph that looks like a polar view of the earth, with the North Pole at the graph's center. The first amplitude value is used as an angle -- 40 degrees -- and the second number as a distance -- 30 units -- from the pole or zero-point. That combination marks one spot on the graph.

To mark a second spot, the second number in the data set becomes the angle (30 degrees) and the third number represents the distance (35 units). The process is repeated until all the amplitude values are accounted for. To create the snowflake-like pattern, the resulting array of dots, which fills roughly one-sixth of the full graph, is reflected as in a kaleidoscope. The patterns become even more striking with the addition of color to indicate which points were plotted earlier and which ones came later.