New #Math 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

remix of d/14855 by u/taupelink

function u(t) {

c.width=500;p=37;a=(t|0)%(p-1)+1;for(n=0,m=a;++n<=p;m*=a,m%=p)x.fillStyle=R((n-1)%(p-1)?0:255,0,(n-p+1)?0:255),x.fillText(n,12+m*12,7+n*7)

Jul 6 2019 6:29 PM UTC

}// 138/140

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Powers of a=1, 2, 3, ..., 36 modulo 37, arranged in rows. The 36th power is always 1; the 37th is a.

u/taupelink

#math #numbertheory Fermat's little theorem https://en.wikipedia.org/wiki/Fermat's_l…
u/DataMeta

Cool!

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taupelink

function u(t) {

t||(a=[J=64]);c.width=160
for(i=64;i--;)t||(a[i]=i),x.fillText(a[i],i%8*20,9+(i>>3)*9)
J&&(K=Math.random()*(J--)|0,[a[K],a[J]]=[a[J],a[K]])

Jul 5 2019 3:29 AM UTC

}// 139/140

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Fisher-Yates shuffle aka Knuth shuffle. #math https://en.wikipedia.org/wiki/Fisher%E2%80%9…

u/taupelink

I'd be curious to see how much space can be saved by golfing on this one!
u/Xen

killed 8bytes for you
u/taupelink

#shuffle

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taupelink

function u(t) {

t||(c.width=162,r=X=4567,s=Y=89,h=l=n=1,i=k=0)
r&&x.fillText(h+`x${X}+(${k})x${Y}=`+r,0,n++*9),q=r/s|0,[h,k,r,i,l,s]=[i,l,s,h-q*i,k-q*l,r%s]

Jul 1 2019 4:45 AM UTC

}// 140/140

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Extended Euclidean algorithm, to find h, k such that hX+kY=gcd(X,Y) #math #numbertheory

u/durian-favored-monster

i remember this in high school it was very cool! good job! this is the best text one i've seen
u/geb

EEA is so cool!

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taupelink

function u(t) {

c.width=500;p=37;a=2+t|0;for(n=0,m=a;++n<=p;)x.fillStyle=R((n-1)%(p-1)?0:255),x.fillText(n,270+(k=40+n)*C(z=m*6.28/p),140-k*S(z)),m*=a,m%=p

Jul 1 2019 1:21 AM UTC

}// 139/140

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Demonstration of Fermat's little theorem. Powers of 2, 3, 4..., modulo 37, arranged around a circle broken up into 37 equal arcs. #math #numbertheory https://en.wikipedia.org/wiki/Fermat%27s_lit…

u/donbright

p is 37?
u/taupelink

Yep, I picked an arbitrary prime number for demonstration purposes
u/donbright

awesp,e

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joeytwiddle

remix of d/14824 by u/donbright

function u(t) {

c.width=400
d=(r,T)=>x.fillText(T,200+r*S(a=i/1.91),115-r*C(a))
for(i=N=t|0;i>1;i--)
for(N%i||d(60+i,i),k=50;k--;)N%i||d(k,'*')

Jun 29 2019 4:36 AM UTC

}// 127/140

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Prime factors on a clock #primes #math

Show more comments…
u/joeytwiddle

Shouts to donbright and taupelink!
u/joeytwiddle

35, 55, 77, 95, 115 and 119 all draw a lambda
u/katkip

Wow
u/taupelink

yay
u/DataMeta

Noice!
u/joeytwiddle

Oops this shows all factors, not just prime factors
u/donbright

hee hee sorry my description on the original was slightly misleading
u/donbright

you have golfed it down to where you might actually be able to do something only with prime factors
u/donbright

holy smokes... i just realized something. if you express an integer using this method, there are only 2 to the twelfth possible representations, which is 4096
u/joeytwiddle

Even fewer, since 4, 6, 8, 9, 10, and 12 never appear alone
u/joeytwiddle

They all light up at t=13860, after 3.85 hours #waitforit
u/joeytwiddle

For seconds/minutes use S(a=i/9.55) and d(60+i/4,i)
u/joeytwiddle

To see factors of odd numbers only, and quickly: i=N=t*22|1
u/donbright

cool

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donbright

remix of d/14804 by u/taupelink

function u(t) {

c.width=400
for(i=N=t>>33<<32;i>0;i--)
for(k=90;k--;){U=200+k*S(t+i)
V=99+k*C(t+i)
N%i?0:k>80?(x.fillText(i,U,V),k=80):x.fillRect(U,V,2,2)}

Jun 28 2019 11:57 PM UTC

}// 139/140

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prime o'clock in the morning

u/donbright

thanks to @taupelink for inspiration
u/taupelink

yay!
u/joeytwiddle

Fascinating! #primes #math U=200+k*S(a=i/1.91),V=99-k*C(a)

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13thptr

function u(t) {

h=N=M=0
for(i=18;i--;x.stroke(new Path2D(`M500 500L${M+(b=500)} ${N+b}L${O+b} ${P+b}`)))O=M,P=N,M=C(h+=Math.atan2(99,r=i**.5*99))*r,N=S(h)*r

Jun 28 2019 9:33 PM UTC

}// 140/140

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Spiral of Theodorus

u/donbright

awesome
u/13thptr

#spiral #math #path2d
u/13thptr

Thanks to u/joeytwiddle for the golfing help

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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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