A key question is how to measure the level of disorder in the patterns. Without such a measure, it is impossible to compare different patterns or to determine if a pattern is becoming more or less disordered with time. The image shows contours of constant phase in the pattern. White lines indicate parts of the pattern where fluid is stationary. Orange and Blue lines indicate parts of the pattern where fluid is rising or falling, respectively.
Defects occur when the contour lines cross each other.
We have now developed such a method. A mathematical technique called complex demodulation is used to generate an idealized representation of the pattern called the order parameter. The order parameter can be regarded as a map of locations where the fluid is rising, falling and at rest. The image above shows an enlargement of the upper left portion of the pattern. In the organized parts of the pattern, the regions of rising and falling fluid are arranged in parallel lines.