Tupper’s self-referential formula – Wikipedia
Tupper’s formula is an inequality created by Canadian Jeff Tupper that generates a pattern of 17×106 pixels from a given number.
Depending on the parameter, all possible pixel patterns of size 17×106 can be generated. In particular, the formula itself can be represented as a pixel pattern using a suitable parameter. This led to the sometimes used term “Tupper’s self-referential formula”.
This image is to be created with the following number k: 4 858 450 636 189 713 423 582 095 962 494 202 044 581 400 587 983 244 549 483 093 085 061 934 704 708 809 928 450 644 769 865 524 364 849 997 247 024 915 119 110 411 605 739 177 407 856 919 754 326 571 855 442 057 210 445 735 883 681 829 823 754 139 634 338 225 199 452 191 651 284 348 332 905 131 193 199 953 502 413 758 765 239 264 874 613 394 906 870 130 562 295 813 219 481 113 685 339 535 565 290 850 023 875 092 856 892 694 555 974 281 546 386 510 730 049 106 723 058 933 586 052 544 096 664 351 265 349 363 643 957 125 565 695 936 815 184 334 857 605 266 940 161 251 266 951 421 550 539 554 519 153 785 457 525 756 590 740 540 157 929 001 765 967 965 480 064 427 829 131 488 548 259 914 721 248 506 352 686 630 476 300
Generalization of Tupper’s formula
As part of her Bachelor’s thesis at the University of Bremen, Ellen Rudolph generalized Tupper’s formula in such a way that multicoloured images can be displayed, which can also be of any height and width. It is also shown how the corresponding definition area for the generalized formula is determined for each image so that the formula generates the image at this point in the coordinate system.