Tupper's self-referential formula: Difference between revisions

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.,

${\displaystyle {1 \over 2}<\lfloor \mathrm {mod} (\lfloor {y \over 17}\rfloor 2^{-17\lfloor x\rfloor -\mathrm {mod} (\lfloor y\rfloor ,17)},2)\rfloor ,}$

and 0 ≤ x ≤ 105, n ≤ y ≤ n + 16 where

n = 9609393799189588849716729621278527547150043396601293066515055192717

0280239526642468964284217435071812126715378277062335599323728087414

4307891325963941337723487857735749823926629715517173716995165232890

5382216124032388558661840132355851360488286933379024914542292886670

8109618449609170518345406782773155170540538162738096760256562501698

1482083418783163849115590225610003652351370343874461848378737238198

2248498634650331594100549747005931383392264972494617515457283667023

6974546101465599793379853748314378684180659342222789838872298000074

8404719.

The plot of the formula is as follows:

where the above inequality is true, a black pixel is plotted.