Self Referential Formula, Plot your name!

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 1,802-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 ;)

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Self Referential Formula, Plot your name!

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