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.

Try the new frontend: beta.dwitter.net
Current theme challenge: #Opposites

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KilledByAPixel

function u(t) {

eval(unescape(escape`𭀿𫰽𘠢𞡣𛡯𭑴𩑲𢁔𣑌🐢🁤𪑶𘁩𩀽𣰾🀯𩁩𭠾🐾🁩𫡰𭑴𘁩𩀽𢐾🀽𘠻𒡩👉𛡶𨑬𭑥𞱦𫱲𚁪🐱𜀱𞱪𛐭𞱏𛡩𫡮𩑲𢁔𣑌👯𚑔𦱪𧐿𫰽𪠫𨀽𙁻𥁛𪡝𯐠𨀫𫰺𪐮𫑡𭁣𪀨𛱞𦰭𚰪𚀩𛰮𝁝𚠤𛱧𚐦𙡩𛡭𨑴𨱨𚀯𝀯𩰩𛡬𩑮𩱴𪀽🐴𙠦𚁶👥𭡡𫀨𪐩𚐽👶𯀰🱔𦱶𧐽𪐺𜀻`.replace(/u../g,'')))

Aug 13 2019 5:19 AM UTC

}// 140/140

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our Fours Puzzle V2 ~ How many integers between 0-100 can you form using only 4 4s and the +-*/.() operators? Example 1=44/44

u/KilledByAPixel

Updates: Fix issue with space running out after 20. You can also use the decimal point. Only exact matching strings are accepted.
u/KilledByAPixel

#interactive #math #puzzle #game

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taupelink

remix of d/15380 by u/taupelink

function u(t) {

g=(a,b)=>b?g(b,a%b):a;f=()=>Math.random()*1e7|0;t||(m=n=0);n++;g(f(),f())-1||m++;x.fillRect(n%1920,1080*(1-m/n),1,1);throw m/n

Aug 11 2019 4:25 AM UTC

}// 126/140

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If you take two random integers of at most 7 digits each, what is the probability that they are relatively prime? This simulation suggests somewhere around 60%

u/taupelink

In the graph, the x-axis shows number of trials, modulo 1920 (i.e. with wraparound). The y-axis shows % of trials with GCD 1, with 0% at bottom and 100% at top.
u/taupelink

After a little Web searching: Under more general conditions, the precise answer appears to be 6/π^2, or about .608. See, e.g., https://www.cut-the-knot.org/m/Probability/T…
u/aleamb

#math

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taupelink

remix of d/14804 by u/taupelink

function u(t) {

f=X=>{for(i=2;i*i<=X;i++)if(X%i==0)return i+'*'+f(X/i);return X};frame%30||(c.width=200,q=f(k=Math.random()*1e9|0),x.fillText(k+'='+q,5,60))

Aug 11 2019 12:34 AM UTC

}// 140/140

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Factorization of a random integer into #prime products

u/aleamb

awesome! #math #numbers #primes

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katkip

function u(t) {

t||(k=0);for(j=2000;j--;){i=parseInt(k.toString(2).split``.reverse().join``,2);x.fillRect(k%1920,1080-i%1080,1,1),k++}

Aug 8 2019 3:01 PM UTC

}// 118/140

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reverse binary sequence graph #math #binary

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monstrousmoonshine

function u(t) {

c.width*=1,x.globalAlpha=.5;for(i=41;i--;x.stroke())p=300/C(v=.3*t+.1571*i),q=p*S(v),x.beginPath(),x.arc(960+p,540-q,Math.sqrt(p*p+q*q),0,7)

Jul 25 2019 3:40 PM UTC

}// 140/140

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Lemniscate

u/donbright

#math
u/KilledByAPixel

👍

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taupelink

function u(t) {

t||(x.font=`30em"`,x.fillText("1+",40,620),x.fillText("1",1050,400),x.fillRect(570,b=450,1200,24))
x.drawImage(c,0,0,2e3,1e3,650,b,1100,550)

Jul 24 2019 3:24 AM UTC

}// 140/140

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Continued fraction for the golden ratio, 1+sqrt(5)/2. #math #numbertheory https://en.wikipedia.org/wiki/Golden_ratio

u/taupelink

hmm, doesn't seem to work on iOS Safari
u/taupelink

to get it to work on iOS/MacOS, replace 2e3 with 1920 and 1100 with 1e3.
u/taupelink

* maybe it's a safari issue rather than an OS issue. * on my iOS device, that adjustment seems to work temporarily, but then the browser has to reload the screen. ¯\_(ツ)_/¯

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taupelink

remix of d/15085 by u/taupelink

function u(t) {

t||(A=[e=512,e+1],r=i=n=2);i--?(z=A[i],N=z%e,D=z>>9,x.fillText(N+'/'+D,N/D*1900,D*9),n-i-1&&A.splice(i+1,0,w+z),w=z):(i=n+=n-1)

Jul 22 2019 12:55 AM UTC

}// 127/140

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Farey sequence #math #numbertheory

u/donbright

awesome
u/IV

called Farey because wings? :)

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taupelink

function u(t) {

t||(A=[e=1<<9,e+1],r=i=n=2,q=s="");i--?(z=A[i],s=`${z%e}/${z>>9} `+s,n-i-1&&A.splice(i+1,0,w+z),w=z):r++<12&&(q=s,i=n+=n-1,s="")
throw q

Jul 22 2019 12:30 AM UTC

}// 136/140

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Farey sequence of rational numbers. #math #numbertheory https://en.wikipedia.org/wiki/Farey_sequence

u/taupelink

a/b+c/d is NOT equal to (a+b)/(c+d), but the latter quantity is known as the "mediant" and is of interest. https://en.wikipedia.org/wiki/Mediant_(mathe…
u/taupelink

See also https://www.dwitter.net/d/14451 by u/KilledByAPixel
u/KilledByAPixel

👍
u/donbright

I did a Ford's Circles dweet a while back, https://www.dwitter.net/d/1951 ... love this stuff

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joeytwiddle

remix of d/14827 by u/joeytwiddle

function u(t) {

c.width=600
d=(r,T)=>x.fillText(T,300+r*S(a=i/9.55),172-r*C(a))
for(i=N=t|0;i;i--)
for(N%i||d(90+i/4,i),k=75;k--;)N%i||d(k,'*')

Jul 15 2019 7:15 AM UTC

}// 127/140

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Divisors on a clock (second hand version) #math

u/katkip

awesome
u/aleamb

love it!
u/donbright

super cool
u/joeytwiddle

Shouts to u/donbright and u/taupelink

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rodrigo.siqueira

remix of d/12440 by u/rodrigo.siqueira

function u(t) {

t||(a=b=0)
for(i=5e3;i--;)x.fillStyle=R(C(a)*200,S(a)*b/3,t*42),x.fillRect(960+b*S(a*.8),540-b*C(a*.8),1,1),a+=1.9*C(2.5*a)+C(t/5),b+=.00076

Jul 7 2019 9:15 PM UTC

}// 140/140

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Feigenbaum Flower. Homage to Mitchell Feigenbaum (1944-2019). He demonstrated the universal character of dynamical non-linear systems, which has made possible the systematic study of chaos. In 1975, using the small HP-65 calculator, he discovered that the ratio of successive distances between bifurcation events tends to a constant δ ≈ 4.66920... This "ratio of convergence" of period-doubling bifurcations is now known as the first Feigenbaum constant. #bifurcation #attractor #fractal #chaos #math

u/taupelink

This is a great tribute. RIP.
u/donbright

really nice
u/artfarnaa

Rodrigo - are you working full time on this fractal stuff? Super impressive if its only a hobby. Great work.
u/rodrigo.siqueira

#tribute

dwitter.net | #Math