Hello Guys;
I wrote a note before that about a website that where you can graph your name.
Today I'll present to you this formula :
\[ \frac{1}{2} < \left\lfloor \bmod\left(\left\lfloor\frac{y}{17}\right\rfloor2^{17\lfloor x\rfloor  \bmod(\lfloor y \rfloor, 17)}, 2\right)\right\rfloor \]
its name is Tupper's Self Referential Formula and the best part of this is that when we plot it in certain range the graph is the formula itself
Amazing isn't it and the number \(N\) is equal to:
 N=4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024915119110411605739177407856919754326571855442057210445735883681829823754139634338225199452191651284348332905131193199953502413758765239264874613394906870130562295813219481113685339535565290850023875092856892694555974281546386510730049106723058933586052544096664351265349363643957125565695936815184334857605266940161251266951421550539554519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300

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 1,802digit binary number. If you convert that number into base10, 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 \(N\):
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48  #!/usr/bin/env python
# * coding: utf8 *
"""
Plot Tupper's selfreferential 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, widerapart 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
@ChewSeong 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 ;)
Comments
Sort by:
Top NewestOkay, my understanding is that a "selfreferential 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 selfreproduction? 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. – Michael Mendrin · 1 year, 11 months ago
Log in to reply
I saw this on Numberphile – Aditya Chauhan · 1 year, 11 months ago
Log in to reply
– Kaito Einstein · 1 year, 11 months ago
Yes they made a video about i think He was Matt Parker who made itLog in to reply
– Aditya Chauhan · 1 year, 11 months ago
Yeah matt parker it wasLog in to reply
Nice. I just found about the function (here's the graph  desmos).
Here's an interesting link  tupper formula – Arulx Z · 1 year, 3 months ago
Log in to reply
Calvin Lin ChewSeong Cheong Maggie Miller Jake Lai Pi Han Goh – Kaito Einstein · 1 year, 11 months ago
Log in to reply
– Anish Harsha · 1 year, 11 months ago
Can you please do it in my name too ? In the comment box !Log in to reply
– Kaito Einstein · 1 year, 11 months ago
ok no problem but it will take some time, maybe after 4 hours :)Log in to reply
– Anish Harsha · 1 year, 11 months ago
ThanksLog in to reply
Log in to reply
– Anish Harsha · 1 year, 11 months ago
Great Work , Kaito !Log in to reply
– Kaito Einstein · 1 year, 11 months ago
Thanks :)Log in to reply
Dude , Amazing! SuperLike :) – Nihar Mahajan · 1 year, 11 months ago
Log in to reply
Jk Great work! @Kaito Einstein – Mehul Arora · 1 year, 11 months ago
Log in to reply
– Nihar Mahajan · 1 year, 11 months ago
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. :) – Mehul Arora · 1 year, 11 months ago
Log in to reply
– Nihar Mahajan · 1 year, 11 months ago
Nothing sentimental in that. Since you had got the wrong reason ,I just gave the right reason why I posted that comment.Log in to reply
– Mehul Arora · 1 year, 11 months ago
Okay dude, Relax!Log in to reply
– Nihar Mahajan · 1 year, 11 months ago
I am already relaxed (for some time) :)Log in to reply
– Mehul Arora · 1 year, 11 months ago
Good to know. :)Log in to reply