The Worlogog is part of the cosmology of the Fourth World, and apparently native to Earth.
The New God Metron used it to transport a group of Justice Leaguers and super villains from Apokolips through several other dimensions to Earth. It was later manipulated in Zero Hour by the villain Extant to cause disturbances in the Time Stream in 1994.
During the "Rock of Ages" it was found by Lexcorp's "acquisitions department" in the possession of a Colombian drug baron who was using it as a paperweight. Upon his death, it was stolen by Lexcorp and examined by Lex Luthor. Since it was resonating in sync with the thought-patterns of an alien in Lexcorp's custody, he used it to control the alien in part of a plot against the JLA. However, he soon discovered that the object's power was far greater: it reacted to all thought, and could alter reality.
Metron arrived, and told the heroes the deeper truth - the Worlogog was a map of the universe in four dimensions, and allowed the user a certain degree over time and space. In one possible future, its destruction allowed Darkseid to conquer the universe totally.
The Worlogog was eventually turned over to Hourman of Justice Legion A, in his role as Metron's successor. Part of its power was stolen by Amazo, and the two androids chased each other through time before Hourman regained the Worlogog's full power. Hourman may have been wearing the Worlogog when he died at the hands of Extant.
The Worlogog temporarily fell into the hands of Vera Black when she was under the control of a mental copy of Manchester Black, taking a humanoid form for the first time. It was used to cause great destruction by Manchester, until Vera's control was regained and the lives lost restored.
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