Snowflake in the same micro-environment does not guarantee that each arm grow the same; indeed, for some crystal forms it does not because the underlying crystal growth mechanism also affects how fast each surface region of a crystal grows. Empirical studies suggest less than 0.1% of snowflakes exhibit the ideal six-fold symmetric shape. Very occasionally twelve branched snowflakes are observed; they maintain the six-fold symmetry. Snowflakes form in a wide variety of intricate shapes, leading to the notion that "no two are alike". Although nearly-identical snowflakes have been made in laboratory, they are very unlikely to be found in nature. Initial
Symmetrical components for three phase voltage components can be written as and decomposing the vector into three symmetrical components gives where the subscripts 0, 1, and 2 refer respectively to the zero, positive, and negative sequence components. The sequence components differ only by their phase angles, which are symmetrical and so are formula_3 radians or 120°. Define a phasor rotation operator alpha, which rotates a phasor vector counterclockwise by 120 degrees: Note that α = 1 so that α = α. The zero sequence components have equal magnitude and in phase with each other, therefore: and the other phase sequences have the