Mills' Mess Mills' Mess In toss juggling, Mills Mess is a popular juggling pattern, typically performed with three balls although the props used and the number of objects can be different. The pattern was invented by and named after Steve Mills. It is a well-known trick among jugglers and learning it is considered somewhat of a milestone, "a mind-boggling pattern of circling balls, crossing and uncrossing hands, and unexpected catches." The base of this pattern is a traditional reverse cascade, (siteswap 3 in siteswap notation), with an extra "mess" added by crossing and uncrossing arms. The effect created is that the balls
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