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

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

Page image

RELATED LINKS

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