Tupper's Self-Referential Formula

http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html

by guava • 11 years ago

25 12 11 years ago

mathworld.wolfram.com

guava• 11 years ago

Numberphile video about this formula: https://www.youtube.com/watch?v=_s5RFgd59ao

cousin_it• 11 years ago

Sorry, it ain't self-referential unless it draws the picture around (0, 0).

I have no idea if that's possible, though. Quines are possible in many programming languages, but the "language" of formulas without quantifiers is very limited. You can encode boolean logic, not sure about loops.

EDIT:

After some Googling, I've found a true self-referential formula: http://jtra.cz/stuff/essays/math-self-reference/index.html

Note that it involves a recursive function definition, and part of the formula is generated by a fixpoint trick. I suppose that's the simplest way to do this.

Also I really enjoyed the way he embedded a watermark into the formula, in a way that's difficult to remove if you don't know what you're doing.

userbinator• 11 years ago

Quines are possible in compression algorithms too: http://research.swtch.com/zip

Combining that with a self-referential formula could conceivably lead to something like a formula that generates a compressed zipfile, whose contents are a bitmap image of the formula...

xamuel• 11 years ago

Self-referential formulas (truly self-referential ones, not involving the magic constant in Tupper's famous one) are conceptually a consequence of Kleene's recursion theorem, just like self-printing programs, but with a bit more caveats---obviously necessary caveats since it all depends on things like font choice etc. I spelled the details out in a paper [1] but there's really nowhere appropriate to publish it, since it's too trivial for a mathematician/computer scientist audience and too tricky for a more general audience.

[1] http://semitrivial.com/papers/eqn.pdf

netrus2• 11 years ago

Hm, to me this feels scammy, like the 'my-crack-is-nothing-but-the-32894239487th-prim'-trick. Count me impressed as soon as the plot also contains the input range ;)

netrus2• 11 years ago

2^(106*17) only has 543 decimal-digits. So with a high likelyhood, the formular will plot "this is so wrong" in several basic fonts and languages for smaller n's as an input.

virtualSatai• 11 years ago

You have a pixel grid of 17 x 106, anything you want to drawn in it can be.

To draw an arbitrary figure do this: Start with the pixel in the lowest left corner, if black put 1 as the first digit of a binary number else put 0, then continue first up then one right, the down. Convert this (1802 digit) binary number to decimal and use it as input for the function and there it is.

ExpiredLink• 11 years ago

No Tupperware? I'm disappointed.

raldi• 11 years ago

A true quine graph would have to include the "N" constant, too.

andrelaszlo2• 11 years ago

Tupper, Jeff. "Reliable two-dimensional graphing methods for mathematical formulae with two free variables." Proceedings of the 28th annual conference on Computer graphics and interactive techniques. ACM, 2001.

http://www.dgp.utoronto.ca/papers/jtupper_SIGGRAPH2001.pdf

alexdowad• 11 years ago

How did "Tupper" figure this formula out??? Brute force?

andrelaszlo2• 11 years ago

Nope!

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Tupper's Self-Referential Formula

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