File:Checkered quadrant colors in 2-cube matrix.svg

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file ‎(SVG file, nominally 300 × 300 pixels, file size: 2 KB)

Captions

Captions

Add a one-line explanation of what this file represents

Summary[edit]

Description
general

A Boolean function has parity and depravity.
It is even, iff the first digit of the truth table is false. (Its Zhegalkin index is also even.)
It is evil, iff the last digit of the truth table is false. (Its Zhegalkin index has even binary weight.)

even evil (0) even odious (2)
odd evil (1) odd odious (3)


noble

All noble Boolean functions are even.
But they are also partitioned into quadrants. The place of parity is taken by strength.
There are as many n-ary nobles as there are (n−1)-ary Boolean functions. (E.g. the number of 3-ary nobles is 16.)
The nobles sorted by size are the rows of table Sloane's A358167.
The indices to this row can be assigned general quadrants (because integers can be interpreted as truth tables).
The general quadrants of the indices are equal to the noble quadrants of the entries.

weak evil (0) weak odious (2)
strong evil (1) strong odious (3)
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current13:11, 10 June 2023Thumbnail for version as of 13:11, 10 June 2023300 × 300 (2 KB)Watchduck (talk | contribs)Uploaded own work with UploadWizard

You cannot overwrite this file.

The following page uses this file:

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Checkered_quadrant_colors_in_2-cube_matrix.svg&oldid=855233917"