The continuously swirling pattern of expanding and contracting circles, visible on a display screen at Mr. Spock's Library Computer Station, is called a Moire pattern and was an enlarged but identical version of the special effect that was utilised on the working communicator hand prop seen in the 2nd season episode "Friday's Child".
The exact pattern was taken from one of the moires published in the 1964 booklet from Edmund Scientific called "The Science of Moire Patterns" by Dr. Gerald Oster. (The static patterns seen on the non-working or dummy TOS communicator props also came from this same source.) The front and back booklet covers are shown below ...
The special effect seen at Spock's station was created using Pattern No. 4 ...
Basically, the dynamic swirling motion was achieved by overlaying one copy of the moire pattern that was printed on a transparency over a duplicate copy printed on glossy solid card stock; with the centers of the 2 patterns slightly offset; and then revolving the one pattern roughly a single revolution every 30 seconds.
It is known that a stopwatch powered the small moire effect in the hero communicator.
In 1997, respected TOS collector and expert John Castillo visited James Rugg, the Supervisor of Special Effects for The Original Series, at his home in Vista, California. Mr. Rugg indicated that the Science Station moire was driven by a motor and he stated that it made alot of noise during filming. He also said that the reason the moire does not move in later episodes of Star Trek is that the motor broke, and when he went to fix it - he was told to never mind doing the repair since it made too much noise anyway!
Sadly, James Rugg passed away in 2004 from complications due to Alzheimer's disease. He was 85 years old. In 1997, Mr. Rugg; who had received a 1966-67 Emmy award nomination for his special effects work on Star Trek; still had some momentos from his days on the Desilu soundstage. Included in his collection were the alien phaser weapons used by the royal guards that accompanied "Elaan of Troyius" onto the Enterprise, in the 3rd season episode of the same name; several rectangular aircraft switches used on different Enterprise control panels; some spare transparency prints of the Spock Station Moire pattern; and a large binder filled with detailed photographs showing all of the components for the various mechanisms on the Star Trek Bridge set and other Desilu Trek soundstage set fixtures - in unassembled and assembled state. Also on display was a large home-made lamp, consisting of a large sphere (described by John Castillo to be about the size of the spheres containing the Sargon and alien entities from the 2nd season episode "Return to Tomorrow") over the entire surface of which had been glued many multicolor square and round resin buttons which - Mr. Rugg confirmed - were original control panel buttons used on the Enterprise Bridge set at Desilu.
Below is a photo of Jim Rugg taken at the 1997 visit. Many thanks to John Castillo for sharing his recollections of an exciting afternoon spent with one of the ingenious creators of Star Trek.
