Binary Patterns of Integer Functions

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
Intricate patterns can be produced from the binary number representation of the results of integer functions. Is there a cellular automata rule (and initial condition) that can produce the same behavior and computation?
Contributed by: Daniel de Souza Carvalho (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
There is a cellular automaton (NKS|Online) that computes the primes.
Permanent Citation
"Binary Patterns of Integer Functions"
http://demonstrations.wolfram.com/BinaryPatternsOfIntegerFunctions/
Wolfram Demonstrations Project
Published: March 7 2011