New #numbertheory dweets

function u(t) {

c.width=1920 // clear the canvas
for(i=0;i<9;i++)
x.fillRect(400+i*100+S(t)*300,400,50,200) // draw 50x200 rects

} // 122/140

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    u(t) is called 60 times per second.
    t: Elapsed time in seconds.
    S: Shorthand for Math.sin.
    C: Shorthand for Math.cos.
    T: Shorthand for Math.tan.
    R: Function that generates rgba-strings, usage ex.: R(255, 255, 255, 0.5)
    c: A 1920x1080 canvas.
    x: A 2D context for that canvas.

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taupelink

function u(t) {

c.width|=0;f=X=>{for(i=2;i*i<=X;i++)if(X%i==0)return i+'*'+f(X/i);return X};k=frame/6|0;x.font='5em"';x.fillText(k+'='+f(k),0,540)

Jun 28 2019 1:01 AM UTC

}// 130/140

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factorization into #prime products. #math

u/taupelink

simple #recursion #recursive
u/Xen

very clever
u/katkip

wow
u/donbright

#numbertheory

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andrea270872

function u(t) {

a=~~t
b=~~(t%1*10)
x.setTransform(A=a*9,B=b*9,-B,A,800,600)
for(i=-7;i++<7;)for(j=14;j--;x.fillRect(i,j-7,.05,.05));

Jun 27 2019 8:25 AM UTC

}// 116/140

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Sieve of Eratosthene for Gauss Integers - all white pixels left will be Gauss Primes

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taupelink

remix of d/14770 by u/donbright

function u(t) {

f=frame;g=(a,b)=>b?g(b,a%b):a
e=X=>{n=0;for(i=X;--i;)n+=(g(i,X)==1);return n}
y=e(f);x.fillRect(f,1080-y/2,1,y/2)

Jun 27 2019 12:41 AM UTC

}// 113/140

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Graph of Euler's totient function, a remix that reuses donbright's compact definition of gcd. https://en.wikipedia.org/wiki/Euler%27s_toti…

u/taupelink

#math
u/taupelink

better version? t||(A=[]);f=frame;g=(a,b)=>b?g(b,a%b):a;for(X=0;X++<1920;) {n=0;for(i=X;--i;)n+=(g(i,X)==1);A[X]=n;x.fillRect(X,1080-n/2,1,2e3)}
u/taupelink

better version without gcd: t||(A=[0,1]);for(X=2;X++<1920;) {n=X;for(i=X;--i;)if(X%i==0)n-=A[i];A[X]=n;x.fillRect(X,1080-n/2,1,2e3)}
u/donbright

lol why do i think this looks like a city skyline?
u/donbright

#euler #totient #numbertheory

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taupelink

function u(t) {

f=j=>x.fillRect(448+(j&255)*4,(j>>8)*4,4,4)
t||(p=Array(N=4**8).fill(n=1),f(0),f(1))
if(p[++n])for(i=1;(q=++i*n)<N;)p[q]=0,f(q),M=n;throw M

Jun 19 2019 2:39 AM UTC

}// 139/140

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Sieve of Eratosthenes. Throws primes less than 65536. Row Y Column X stays unfilled if 256*Y+X is prime. #math

u/Xen

clever
u/donbright

#primes #numbertheory
u/taupelink

maybe #sieve is a worthwhile hashtag too!

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taupelink

function u(t) {

t||(a=[[]],r=k=0);x.font=`3em"`
a[r][k]=k%r?a[r-1][k-1]+a[r-1][k]:1
r<16&&x.fillText(a[r][k],960-60*r+120*k,60*r+60)
++k>r&&(a[++r]=[],k=0)

Jun 18 2019 1:17 AM UTC

}// 139/140

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Pascal's Triangle #math #recursive #recursion

u/katkip

Awesome!
u/donbright

#numbertheory

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taupelink

function u(t) {

f=(a,b,n)=>b?(a>=b?
(x.fillStyle=R(25*n),
x.fillRect(X,Y,b,b),X+=d?0:b,Y+=d?b:0,f(a-b,b,n+1))
:(d=!d,f(b,a,n+1))
):0
d=X=Y=0;f(1920,1080,0)

Jun 13 2019 1:58 AM UTC

}// 139/140

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GCD(1920,1080)=120, the size of the smallest reddest square. Demonstration of Euclidean algorithm by subtraction, cf. https://en.wikipedia.org/wiki/Euclidean_algo… #math

u/taupelink

#recursive #recursion
u/taupelink

(120 is the side length, not the size)
u/donbright

#numbertheory
u/donbright

this is super interesting

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KilledByAPixel

function u(t) {

for(s="",a=[i=1];i++<300;s+=a[i-2]+"/"+a[i-1]+"&emsp;")i%2?(n=(i-1)/2,m=n+1,a.push(a[n-1]+a[m-1])):(n=i/2,a.push(a[n-1]))
t?0:c.outerHTML=s

Jun 5 2019 8:36 PM UTC

}// 139/140

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Generating every fraction in order using the Stern–Brocot sequence.

u/KilledByAPixel

Minified version of this https://jan.jarfalk.se/infinite-fractions/
u/taupelink

#math
u/taupelink

#numbertheory
u/KilledByAPixel

https://en.wikipedia.org/wiki/Stern%E2%80%93…

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donbright

remix of d/1871 by u/walsh9

function u(t) {

圈=(n,d,N,D)=>{d+D<15?(圈(n,d,n+N,d+D),圈(n+N,d+D,N,D),w=2e3,m=d+D,x.beginPath(),r=w/m/m/2,x.arc(w*(n+N)/m,r,r,0,7),x.fill()):1}
圈(0,1,1,1)

Mar 7 2017 11:35 PM UTC

}// 136/140

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basic Ford's Circles (sort of like Apollonian Circle Packing but every circle touches the floor, or here, the ceiling)

u/donbright

#math
u/donbright

see also https://www.dwitter.net/d/15086 by @taupelink
u/donbright

#numbertheory
u/taupelink

nice!

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