That's not everything.
The images produced by Tupper’s formula are black and white pictures 106 pixels wide by 17 pixels high. If you take a 106 × 17 grid and place a 1 in the squares you want to be black and a 0 in the squares you want to be white, rotating the image and reading the digits off left to right, working down the image, will give you a 1,802-digit binary number. If you convert that number into base-10, then multiply it by 17, you get the value \(N).

like if we want to plot the name \(KAITO\) we do this:

and this Python code allow you to plot the formula for any integer \(N\):

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
Plot Tupper's self-referential formula
"""
#N = 960939379918958884971672962127852754715004339660129306651505519271702802395266424689642842174350718121267153782770623355993237280874144307891325963941337723487857735749823926629715517173716995165232890538221612403238855866184013235585136048828693337902491454229288667081096184496091705183454067827731551705405381627380967602565625016981482083418783163849115590225610003652351370343874461848378737238198224849863465033159410054974700593138339226497249461751545728366702369745461014655997933798537483143786841806593422227898388722980000748404719
N = 4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024915119110411605739177407856919754326571855442057210445735883681829823754139634338225199452191651284348332905131193199953502413758765239264874613394906870130562295813219481113685339535565290850023875092856892694555974281546386510730049106723058933586052544096664351265349363643957125565695936815184334857605266940161251266951421550539554519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300
H = 17
W = 1
import sys
if __name__ == '__main__':
if len(sys.argv)>1: H = int(sys.argv[1])
def tupper(x,y):
return 0.5 < ((y//H) // (2**(H*x + y%H))) % 2
print "x range: 0 < x <",
W = int(raw_input())
print 'Got width: %d' % W
print "y range: N < y < N+%d, where N = (type 0 for default)" % H,
t = int(raw_input())
if t: N=t
print
import matplotlib.pyplot as plot
plot.rc('patch', antialiased=False)
print 'Plotting...'
for x in xrange(W):
print 'Column %d...' % x
for yy in xrange(H):
y = N + yy
if tupper(x,y):
plot.bar(left=x, bottom=yy, height=1, width=1, linewidth=0, color='black')
print 'Done plotting, please wait...'
plot.axis('scaled')
#For large graphs, must change these values (smaller font size, wider-apart ticks)
buf = 2
plot.xlim((-buf,W+buf))
plot.ylim((-buf,H+buf))
plot.rc('font', size=10)
plot.xticks(range(0, W, 100))
yticks = range(0, H+1, 4)
plot.yticks(yticks, ['N']+['N + %d'%i for i in yticks][1:])
plot.savefig('out.png')
plot.savefig('out.svg')

and Finally i calculate the \(N\) of some names of brilliant's members those who amazed me with their Ideas Problems and Solutions, Hope they don't Mind

starting with brilliant

@Calvin Lin

@Pi Han Goh

@Jake Lai

@Chew-Seong Cheong

@Nihar Mahajan

@Satyajit Mohanty

@Maggie Miller

For the numbers \(N\) for every name you can find them Here

feel free to comment anything any suggest...
See you another time ;)

Okay, my understanding is that a "self-referential formula" is like a mechanism that builds a replica of itself, i.e., it reproduces. If you have a name, and it's rasterized and converted to a number, how is that self-reproduction? Looking at this from a different direction, suppose I have a class of formulas or algorithms in which to generate a sequence of numbers. Further suppose that we have some quote, say, "I am computed, therefore I am". Is it possible to design a formula or algorithm where it is not obvious how that quote could have been "programmed into it", and yet, somewhere in the sequence of numbers, put in raster form, that quote pops out, thus, "I am computed, therefore I am"? Furthermore, how about if that quote is the actual formula being used to generate it? That was Tupper's feat, which is what makes it so interesting.

He plotted my name because I am his friend. Indeed the work is quite amazing and even if my name was not plotted , my opinion would remain unchanged.I hope this changes your view too. :)

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestOkay, my understanding is that a "self-referential formula" is like a mechanism that builds a replica of itself, i.e., it reproduces. If you have a name, and it's rasterized and converted to a number, how is that self-reproduction? Looking at this from a different direction, suppose I have a class of formulas or algorithms in which to generate a sequence of numbers. Further suppose that we have some quote, say, "I am computed, therefore I am". Is it possible to design a formula or algorithm where it is not obvious how that quote could have been "programmed into it", and yet, somewhere in the sequence of numbers, put in raster form, that quote pops out, thus, "I am computed, therefore I am"? Furthermore, how about if that quote is the actual formula being used to generate it? That was Tupper's feat, which is what makes it so interesting.

Log in to reply

I saw this on Numberphile

Log in to reply

Yes they made a video about i think He was Matt Parker who made it

Log in to reply

Yeah matt parker it was

Log in to reply

Nice. I just found about the function (here's the graph - desmos).

Here's an interesting link - tupper formula

Log in to reply

Calvin Lin Chew-Seong Cheong Maggie Miller Jake Lai Pi Han Goh

Log in to reply

Can you please do it in my name too ? In the comment box !

Log in to reply

ok no problem but it will take some time, maybe after 4 hours :)

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Dude , Amazing! SuperLike :)

Log in to reply

Only coz he plotted your name too :P

Jk Great work! @Kaito Einstein

Log in to reply

He plotted my name because I am his friend. Indeed the work is quite amazing and even if my name was not plotted , my opinion would remain unchanged.I hope this changes your view too. :)

Log in to reply

@Nihar Mahajan Tum toh senti ho gye yaar :3

I was just joking man! Each member of the community is everyone's friend. :)

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply