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:
“Have you no beginning and end? Which heart is
the real one? Which eye the seer?”
—Anne Sexton (1928–1974)
“What we do is as American as lynch mobs. America has always been a complex place.”
—Jerry Garcia (1942–1995)
“Think of the earth as a living organism that is being attacked by billions of bacteria whose numbers double every forty years. Either the host dies, or the virus dies, or both die.”
—Gore Vidal (b. 1925)