The Haar wavelet. Replacement for ASCII art:

           |
         1 ****O
           |    
           |   1/2 
   0  *****O---+---*****
           |        
           |        
        -1 |   ****O
           0    

See Wikipedia graph-making tips.

Generated in gnuplot with the following script:

 

The source code of this SVG is invalid due to 4 errors.

 

This W3C-invalid plot was created with Gnuplot.

Then I opened the resulting SVG file in Inkscape, changed the fill style for the circles (either blue or white fill), line styles (to do dashed lines), brought the plot lines to the top, and then brought the circles to the top (over the lines).

Created by User:Omegatron using gnuplot, possibly with post-processing in the GIMP (PNG) or Inkscape (SVG)

I, the copyright holder of this work, hereby publish it under the following licenses:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic 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.

https://creativecommons.org/licenses/by-sa/3.0CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

You may select the license of your choice.

(In short, this means that you can copy and modify the image freely as long as you provide attribution; preferably in the form of a link back to this page.)

• Mathworld article