Tupper's Formula Tools

[+] About Tupper's (self-referential) formula

Tupper's self-referential formula is a formula defined by Jeff Tupper that, when graphed in two dimensions
at a very specific location in the plane (...) visually reproduces the formula itself.
// Actually, it reproduces all possible images that are 106 pixels wide and 17 pixels high.

The formula is an inequality defined by:

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

where ⌊ • ⌋ denotes the floor function, and mod is the modulo operation.

Read more on Wikipedia...
Watch "Numberphile" episode about The 'Everything' Formula (yes, axes directions are wrong...)

Graph

[+] Graph options and functions

Choose color for the first mouse button:

Invert axes

(white/black → black/white)

Produces smaller 'k' number (move right when axes are inverted, left otherwise)

Plot method: Smart - plot graph using knowledge of how Tupper's formula work
Unit-precise - plot graph calculating value for each square unit (very slow, might take a few minutes and freeze browser for a while, better use "Smart" method instead)
Pixel-precise - plot graph calculating value for each pixel (cheating, because thanks to floor function and small optimization all calculations are the same as for previous option)

Number

[+] Number options and functions

Transform binary number (17 rows of 106 binary digits) into graph. Useful to import binary "image" from Excel, Calc, *.txt file, etc.

[+] Intermediate values