Mills' Mess objects, the pattern is adaptable to rings, clubs, torches and a variety of other juggling props. Four-, five-, and (recently) six- and seven-ball variations of these patterns have also been performed, as well as four, five and six clubs. Rubenstein's Revenge is a heavily embellished and distorted Mills Mess. It is one of the most famous Mills Mess variations. The Boston Mess is a variant of Mills Mess in which the arms similarly cross and uncross, but the balls are thrown in columns. It is performed with three balls in a columnar cascade pattern (siteswap 3). Cherry Picking is a
All-pass filter same angle but have reciprocal magnitudes (i.e., they are "reflections" of each other across the boundary of the complex unit circle). The placement of this pole-zero pair for a given formula_9 can be rotated in the complex plane by any angle and retain its all-pass magnitude characteristic. Complex pole-zero pairs in all-pass filters help control the frequency where phase shifts occur. To create an all-pass implementation with real coefficients, the complex all-pass filter can be cascaded with an all-pass that substitutes formula_14 for formula_9, leading to the Z-transform implementation which is equivalent to the difference equation where formula_18 is the