

Tupper's Self-Referential Formula - guava
http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html

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cousin_it
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](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
Quines are possible in compression algorithms too:
[http://research.swtch.com/zip](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...

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xamuel
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](http://semitrivial.com/papers/eqn.pdf)

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guava
Numberphile video about this formula:
[https://www.youtube.com/watch?v=_s5RFgd59ao](https://www.youtube.com/watch?v=_s5RFgd59ao)

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andrelaszlo
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](http://www.dgp.utoronto.ca/papers/jtupper_SIGGRAPH2001.pdf)

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netrus
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
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.

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netrus
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 ;)

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

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

~~~
andrelaszlo
Nope!

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9305641190509942262908344685274700698787904608310595880289812081536724941725545071106206251111889341210627969870351600841061391017216646166285521835238573206095831012695386519407313
2048834858271248011596637678461152511103454279905004053056408200601005093563435521706652553699740157516429165842861194547902262534688997172075774608559464613639019689965790555013120

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ExpiredLink
No Tupperware? I'm disappointed.

