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:
“I came back to myself,
To the real work, to
“What is to be done.””
—Gary Snyder (b. 1930)
“We must open our eyes and see that modern civilization has become so complex and the lives of civilized men so interwoven with the lives of other men in other countries as to make it impossible to be in this world and out of it.”
—Franklin D. Roosevelt (1882–1945)
“One murder makes a villain, millions a hero. Numbers sanctify, my good fellow.”
—Charlie Chaplin (1889–1977)