# Talk:Tupper's self-referential formula

WikiProject Mathematics (Rated Start-class, Low-priority)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Low Priority
Field:  Applied mathematics
WikiProject Computer science (Rated Start-class, Low-importance)
This article is within the scope of WikiProject Computer science, a collaborative effort to improve the coverage of Computer science related articles on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Start  This article has been rated as Start-Class on the project's quality scale.
Low  This article has been rated as Low-importance on the project's importance scale.

## Merge

This should be merged with: http://en.wikipedia.org/wiki/Jeff_tupper_self_referential_formula 132.239.215.69 23:18, 28 January 2007 (UTC)

## two points

you seem to have left out a key point - that the square is white or black depending on if the inequality is satisfied also, where does the x axis value come from ? it seems to just appear

in any event, this whole article could be replaced with this, much better version https://plus.maths.org/content/formula-plots-almost-everything — Preceding unsigned comment added by 2601:192:4701:BE80:28FE:DB8B:5BCF:D23D (talk) 00:53, 24 October 2018 (UTC)

## seems fine now

It seems wiki enough to me. Mathiastck 14:26, 30 January 2007 (UTC)

## Image

Replaced original image; new image is misleading because it has white pixels outside the range of the plot, and this is not the case. Dysprosia 04:52, 3 February 2007 (UTC)

Eh, I don't mind. When I first noticed it, there were two pictures present, and I just chose whichever one looked nicest. --Wafulz 03:46, 4 February 2007 (UTC)

## Misnomer

I'd recommend to directly mention that actually there's nothing self-referential in the formula. It's only a generic decoding formula (as is said later in the article). A 'true' self-referencial formula would not need something like n as input. 131.246.194.46 12:00, 5 July 2007 (UTC)

There's still something self-referential about a formula which plots an ASCII representation of itself over certain inputs. It's not perfect, but I wouldn't go as far as to say it's a misnomer. Chris Cunningham 12:06, 5 July 2007 (UTC)
Stating that "that" is self-referential is the same as stating that a "space" is self-referential because it and its representation are always identical... —Preceding unsigned comment added by Pfortuny (talkcontribs) 11:39, 27 September 2007 (UTC)
That's a bit like saying that a pencil is self-referential because it's possible to use a pencil to draw a picture of a pencil. --Tanner Swett (talk) 19:25, 16 March 2010 (UTC)
I have the same issue: the formula is designed to produce every possible pattern of bitmap rectangles 17 pixels high. The number k is simply about finding where in this mass of patterns, one wich looks vaguely like the formula is. But there are other values of k where the words of the Bible are interleaved with the words of Shakespeare, and others where the text I am typing now can be found.--Rumping (talk) 15:42, 15 March 2011 (UTC)

I agree, there's nothing self-referential about this formula. It's as if someone wrote a program to print out all possible strings in lexicographic order. Yes, such a program would eventually print out its own source code. But no one would call such a program "self-referential", and no one would call it a "Quine". The name of this page should be changed. — Preceding unsigned comment added by 24.27.32.151 (talk) 13:49, 17 August 2012 (UTC)

## Removed claim that Tupper described formula as "totally shocking".

The previous revision claimed Tupper described his formula as "totally shocking" with a reference to http://stanwagon.com/wagon/Misc/bestpuzzles.html . This is a misinterpretation of the content of said webpage. The page lists a series of mathematical games with number 14 being Tupper's formula. The formula is introduced with the wording

14. (Jeff Tupper) There is something about the graph of the following function that is totally shocking. What is it?

The author names Jeff Tupper as a way of attribution, not citation.

## k?

Where is the 'k' symbol in the formula?! Outslider (talk) 20:10, 13 October 2010 (UTC)

In the range definition of y. —Preceding unsigned comment added by 92.224.194.212 (talk) 17:45, 14 January 2011 (UTC)
I’ve moved k into the plot axes for clarity. —Anders Kaseorg (talk) 01:08, 15 August 2013 (UTC)

## Top right corner or bottom left corner?

If k is divided by 17, the least significant bit encodes the top right corner; the 17 least significant bits encode the rightmost column of pixels; the next 17 least significant bits encode the 2nd rightmost column, and so on.

But I think the least significant bit of k/17 is the bottom left corner as in the Cartesian coordinate system. Let x=0 and y=k. Then the right hand side of the formula is mod(k/17, 2). This is the least significant bit and it locates at the bottom left corner. --203.143.165.250 (talk) 05:24, 8 May 2012 (UTC)

There was some confusion here because Tupper’s value of k actually yields an upside-down plot. When you turn it right-side up, the least significant bit actually does encode the top right corner. I’ve fixed this by reversing the axes on the plot and clarifying the article. —Anders Kaseorg (talk) 01:08, 15 August 2013 (UTC)

## The reference list

The original link for reference article Experimental Mathematics in Action is broken, so I find a source with the same name in the same website. To my surprise, the authors listed in the link are not the same as the ones listed here. A source with the same author list is here. Which should be placed here as a source? — Preceding unsigned comment added by Franklin Yu (talkcontribs) 02:51, 23 January 2013 (UTC)

## Images broken

Two of the image links are broken. — Preceding unsigned comment added by 94.215.53.76 (talk) 18:57, 23 April 2015 (UTC)

## Notability?

Why is this non-quine more notable than, say, a typical C quine? // Cachedio (talk) 10:16, 30 April 2015 (UTC)

Answered here, feel free to move it up. #Questioned_of_notability
KING (talk) 04:36, 22 December 2015 (UTC)

## Why should the image be upside down if all bitmaps are possible??

This formula does produce every and all possible bitmaps with 17 pixels height. so, it should contain said formula in all rotations and mirrored in all dorections. why is the example chosen in a way that the formula is upside down (and when you look at the image, both axes are flipped, so it is mirrored left to right too)? Why wasnt an example chosen which initially shows the formula right side up, left to right? 217.9.110.2 (talk) 13:47, 4 May 2015 (UTC)

## The correct value is this 544-digit number!!!

4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865 5243648499972470249151191104116057391774078569197543265718554420572104457358836818298237541396 3433822519945219165128434833290513119319995350241375876523926487461339490687013056229581321948 1113685339535565290850023875092856892694555974281546386510730049106723058933586052544096664351 2653493636439571255656959368151843348576052669401612512669514215505395545191537854575257565907 40540157929001765967965480064427829131488548259914721248506352686630476300 — Preceding unsigned comment added by 49.215.5.60 (talk) 12:40, 19 August 2015 (UTC)

This is the correct number on a Cartesian co-ordinate graph. Tupper's original number is graphed upside down and mirrored probably by mistake due to a conventional Cartesian coordinate graph's y-axis going upwards differing from computers’ screen coordinates' where th y-axis goes downwards. 207.62.184.20 (talk) 23:36, 30 June 2016 (UTC)

## Questioned of notability

Cachedio I am firm in the belief that this program opens every door from mathematics into programming and is notable at least if only for that. More significantly this is a real world example of mathematics having purpose other than practical numbers: you could hypothetically digitize the view of a telescope and plot thereby taking away the need for hand sighting. Seems well enough quoted by text referenced. Those without the textbooks or advanced mathematics can learn and ponder as I did when first introduced - has little significance directly in the appropriate mathematics class and, great significance at that level to the learning world beyond that. KING (talk) 02:08, 21 December 2015 (UTC)

[09:14, 20 December 2015]‎ Cachedio (talk | contribs)‎ . . (5,871 bytes) (+35)‎ . . (I first questioned the notability of this in its talk page about 8 months ago, to no reply. Tag added.)
That makes little sense. By definition, every formula can be plotted with this software (and many other graphical toolboxes) and the appropriate choice of k. The function itself just gives access to the individual pixels, and is not particularly unique or surprising. It is the type of thing any undergraduate with a good understanding of first semester discrete mathematics can produce in a matter of a few hours. It has remarkably little to do with programming. In my opinion, there is nothing notable about this example, and I am inclined to put it up for deletion. // Cachedio (talk) 20:03, 28 December 2015 (UTC)

Hello fellow Wikipedians,

I have just modified one external link on Tupper's self-referential formula. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

As of February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete the "External links modified" sections if they want, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template `{{sourcecheck}}` (last update: 15 July 2018).

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot 22:17, 5 April 2017 (UTC)