Tupper's self-referential formula: Difference between revisions
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'''Tupper's self-referential formula''' is a formula described by its creator, Jeff Tupper, as "totally shocking"<ref>http://stanwagon.com/wagon/Misc/bestpuzzles.html</ref>, because of its property that when plotted within particular ranges, generates a graphical representation of the exact formula used to generate it, viz., |
'''Tupper's self-referential formula''' is a formula described by its creator, Jeff Tupper, as "totally shocking"<ref>[http://stanwagon.com/wagon/Misc/bestpuzzles.html Stan Wagon's "Best Puzzles"], from "Which Way Did the Bicycle Go?", MAA.</ref>, because of its property that when plotted within particular ranges, generates a graphical representation of the exact formula used to generate it, viz., |
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:<math>{1\over 2} < \lfloor \mathrm{mod}(\lfloor {y \over 17} \rfloor 2^{-17 \lfloor x \rfloor - \mathrm{mod}(\lfloor y\rfloor, 17)},2)\rfloor,</math> |
:<math>{1\over 2} < \lfloor \mathrm{mod}(\lfloor {y \over 17} \rfloor 2^{-17 \lfloor x \rfloor - \mathrm{mod}(\lfloor y\rfloor, 17)},2)\rfloor,</math> |
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== References == |
== References == |
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Revision as of 08:39, 21 January 2007
Tupper's self-referential formula is a formula described by its creator, Jeff Tupper, as "totally shocking"[1], because of its property that when plotted within particular ranges, generates a graphical representation of the exact formula used to generate it, viz.,
and 0 ≤ x ≤ 105, n ≤ y ≤ n + 16 where
- n = 9609393799189588849716729621278527547150043396601293066515055192717
- 0280239526642468964284217435071812126715378277062335599323728087414
- 4307891325963941337723487857735749823926629715517173716995165232890
- 5382216124032388558661840132355851360488286933379024914542292886670
- 8109618449609170518345406782773155170540538162738096760256562501698
- 1482083418783163849115590225610003652351370343874461848378737238198
- 2248498634650331594100549747005931383392264972494617515457283667023
- 6974546101465599793379853748314378684180659342222789838872298000074
- 8404719.
References
- ^ Stan Wagon's "Best Puzzles", from "Which Way Did the Bicycle Go?", MAA.