Stephen Wolfram's: A New Kind of Science | Online
Jump to Page
Look Up in Index

Chapter 2 Notes > Section 1 > Page 871 > Note (a) Previous note-----Next note
Notes for: The Crucial Experiment | How Do Simple Programs Behave?

*[Patterns from] bitwise functions

Bitwise functions typically yield nested patterns. (As discussed above, any cellular automaton rule can be represented as an appropriate combination of bitwise functions.) Note that BitOr[x, y] + BitAnd[x, y] == x + y and BitOr[x, y] - BitAnd[x, y] == BitXor[x, y].

The patterns below show where BitXor[x,y]<=t for successive t and correspond to steps in the "munching squares" program studied on the PDP-1 computer in 1962.

Nesting is also seen in curves obtained by applying bitwise functions to n and 2n for successive n. Note that 2n has the same digits as n, but shifted one position to the left.


Page image


Pages related to this note:


All notes on this page:

* [Patterns from] other integer functions
* [Patterns from] bitwise functions
* Tests of randomness
* Rule 30
* Rule 110
* All notes for this section
* Downloadable programs for this page
* Downloadable images
* Search Forum for this page
* Post a comment
* NKS | Online FAQs
From Stephen Wolfram: A New Kind of Science [citation] Previous note-----Next note