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:
“The real drawback to “the simple life” is that it is not simple. If you are living it, you positively can do nothing else. There is not time.”
—Katharine Fullerton Gerould (1879–1944)
“The money complex is the demonic, and the demonic is God’s ape; the money complex is therefore the heir to and substitute for the religious complex, an attempt to find God in things.”
—Norman O. Brown (b. 1913)
“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)