Counterclockwise

Robert P. Munafo, 2008 Mar 14.

When discussing features around the boundary of a mu-atom (for example, the children of the mu-atom, the two directions one can go in while traveling on the boundary are called clockwise and counterclockwise. The same terms can apply to travel along a lemniscate.

Counterclockwise is the direction in which the external angle and/or internal angle get bigger. Clockwise is the direction in which they get smaller.

Internal and external angles increase in the counterclockwise direction because that is the standard definition in trigonometry, calculus, etc. It is an arbitrary decision adopted as standard. It is interconnected with another aribtrary choice, putting the square root of minus one "above" the real axis (rather than "below") — one choice dictated the other. This is also related to the fact that as you proceed from positive real values to positive imaginary values, to negative real values, the imaginary component of the natural logarithm increases.


From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index

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