Iterating On Real or Complex Numbers
The Collatz map can be viewed as the restriction to the integers of the smooth real and complex map
which simplifies to
If the standard Collatz map defined above is optimized by replacing the relation 3n + 1 with the common substitute "shortcut" relation (3n + 1)/2, it can be viewed as the restriction to the integers of the smooth real and complex map
which simplifies to .
Read more about this topic: Collatz Conjecture, Extensions To Larger Domains
Famous quotes containing the words real, complex and/or numbers:
“We must have a real living determination to reach holiness. “I will be a saint” means I will despoil myself of all that is not God; I will strip my heart of all created things; I will live in poverty and detachment; I will renounce my will, my inclinations, my whims and fancies, and make myself a willing slave to the will of God.”
—Mother Teresa (b. 1910)
“In ordinary speech the words perception and sensation tend to be used interchangeably, but the psychologist distinguishes. Sensations are the items of consciousness—a color, a weight, a texture—that we tend to think of as simple and single. Perceptions are complex affairs that embrace sensation together with other, associated or revived contents of the mind, including emotions.”
—Jacques Barzun (b. 1907)
“Green grow the rushes-O
What is your one-O?”
—Unknown. Carol of the Numbers (l. 2–3)