6 ms·
Tupper's Self-Referential Formula
- guava 11y agoNumberphile video about this formula: https://www.youtube.com/watch?v=_s5RFgd59ao https://www.youtube.com/watch?v=_s5RFgd59ao
- cousin_it 11y agoSorry, 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 11y agoQuines 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...
- xamuel 11y agoSelf-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
- netrus 11y agoHm, 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 ;)
- netrus 11y ago2^(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 11y agoYou 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 11y agoNo Tupperware? I'm disappointed.
- raldi 11y agoA true quine graph would have to include the "N" constant, too.
- andrelaszlo 11y agoTupper, 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
- alexdowad 11y agoHow did "Tupper" figure this formula out??? Brute force?
- andrelaszlo 11y agoNope! 6025666355951763778249837815789373723483639790660874583441919736926457025303594218581835796440886522561698107862471237580557765547741317535541261442612598664863666538059646269192885 9305641190509942262908344685274700698787904608310595880289812081536724941725545071106206251111889341210627969870351600841061391017216646166285521835238573206095831012695386519407313 2048834858271248011596637678461152511103454279905004053056408200601005093563435521706652553699740157516429165842861194547902262534688997172075774608559464613639019689965790555013120