Search found 766 matches

by PHPBB12345
Yesterday, 10:38 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

a(1)=2=0^1+2^1=1^1+1^1
a(2)=25=0^2+5^2=3^2+4^2
a(3)=1729=1^3+12^3=9^3+10^3
a(4)=635318657=59^4+158^4=133^4+134^4.
a(5)>1.02*10^26 if exists
by PHPBB12345
July 6th, 2020, 8:03 pm
Forum: The Sandbox
Topic: Ultra-complex logic gates [GAME]
Replies: 23
Views: 617

Re: Ultra-complex logic gates [GAME]

Hi! I don't have enough time to post a new logic gate, but here is the leaderboard: Moosey: 44 points PkmnQ, EvinZL, bubblegum: 18 points EDIT: Here is the new logic gate (Easy) RLE x = 62, y = 44, rule = WireWorld 2.C$.C.2C$2.B2.C$6.9C$4.C10.3C$3.C.2C3.C.C.C3.C$4.B2.C.C.3C4.C$7.C.C 2.C.C.C.C$8.C6....
by PHPBB12345
July 6th, 2020, 12:43 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

Inverse(ProductLog(x)) = x*e^x
Inverse(ProductLog(e^x)) = x+ln(x)
Inverse(e^ProductLog(x)) = x*ln(x)
Inverse(e^ProductLog(ln(x))) = x^x
Inverse(x-ProductLog(e^x)) = x+e^x
by PHPBB12345
July 3rd, 2020, 9:28 pm
Forum: Patterns
Topic: Caterloopillar WIP (all speeds < c/4)
Replies: 155
Views: 154287

Re: Caterloopillar WIP (all speeds < c/4)

yujh wrote:
July 3rd, 2020, 9:25 pm
100c/9300 use in golly, not lv

Code: Select all

Incompleted RLE
by PHPBB12345
June 30th, 2020, 9:04 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

http://oeis.org/A059923/b059923.txt
a(301)=221919095473636555373329715437350019059039490567200027801
a(302)=341500491935765796367892469244602929790811216765676371980
1.538851315191734898742089155195066817888240617677857278408^n
by PHPBB12345
June 29th, 2020, 9:23 pm
Forum: The Sandbox
Topic: Talk to Transformer
Replies: 172
Views: 23457

Re: Talk to Transformer

GUYTU6J wrote:
January 2nd, 2020, 2:01 am
What if we do calculus with T2T? I tried to put these into T2T but I cannot connect.

Code: Select all

Evaluate the following integrals.
    ∫xdx= (1/2)x²+C
    ∫cos xdx= sin x+C
    ∫e^{x}dx= e^{x}+C
    ∫1/(x)dx= ln x+C
    ∫e^{x}/xdx=
∫e^(x)/xdx=Ei(x)+C
by PHPBB12345
June 28th, 2020, 11:33 pm
Forum: Other Cellular Automata
Topic: Miscellaneous Discoveries in Other Cellular Automata
Replies: 1802
Views: 365513

Re: Miscellaneous Discoveries in Other Cellular Automata

Ok, here's a nice one x = 70, y = 20, rule = B2ekn3-aci4-antwy5-ar6-ek78/S1c2-i3-n4-ny5-jk6-e7c8 41b3o10b3o$41b3o10b3o$39b20o$39b20o$39b20o$19b3o19b3o10b3o$19b3o19b3o 10b3o$19b3o19b3o10b3o$19b3o19b3o10b3o$19b3o19b3o10b3o$19b3o19b3o10b3o$ b6o6bob13o13b3o10b3o$ob5o6b2ob12o13b3o10b3o$b6o6bob13o13b3o10...
by PHPBB12345
June 26th, 2020, 9:55 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

sqrt(2) = 5,18 (mod 23) sqrt(3) = 7,16 (mod 23) sqrt(2)+sqrt(3) = 2,11,12,21 (mod 23) sqrt(6) = 11,12 (mod 23) 2*sqrt(6) = 1,22 (mod 23) 5+2*sqrt(6) = 4,6 (mod 23) sqrt(5+2*sqrt(6)) = 2,11,12,21 (mod 23) 2^(1/3) = 16 (mod 23) 2^(1/4) = 8,15 (mod 23) 2^(1/5) = 6 (mod 23) 2^(1/6) = 4,19 (mod 23) 2^(1/...
by PHPBB12345
June 25th, 2020, 9:37 pm
Forum: Other Cellular Automata
Topic: LeapLife (B2n3/S23-q)
Replies: 744
Views: 41927

Re: LeapLife (B2n3/S23-q)

x = 36, y = 18, rule = B2n3/S23-q 12bo21bo$11bo21bo$11b3o19b3o7$4b2o20b2o$3bobo19bobo$3b2o20b2o$b2o20b2o $obo19bobo$2o20b2o$20b2o$19bobo$19b2o! Fuse: x = 152, y = 153, rule = B2n3/S23-q 150bo$149bo$149b3o7$142b2o$141bobo$141b2o$139b2o$138bobo$138b2o$136b2o $135bobo$135b2o$133b2o$132bobo$132b2o$130b...
by PHPBB12345
June 23rd, 2020, 1:59 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

by PHPBB12345
June 22nd, 2020, 3:17 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Continued fraction repeated part

2 1,2 3 1,1,3 1,3 4 2,4 1,1,1,4 1,4 5 2,1,2,5 1,1,5 1,2,2,1,5 1,5 6 3,6 2,6 1,1,1,1,6 1,2,1,6 1,6 7 3,1,1,1,3,7 2,2,7 1,1,7 1,1,1,7 1,3,2,1,1,2,3,1,7 1,7 8 4,8 2,1,3,1,2,8 2,8 1,1,2,1,1,8 1,2,4,2,1,8 1,3,1,8 1,8 9 4,1,1,1,1,4,9 3,9 2,2,1,4,4,1,2,2,9 1,1,9 1,1,1,1,1,9 1,2,1,1,2,1,9 1,4,2,2,4,1,9 1,9...
by PHPBB12345
June 21st, 2020, 2:23 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

Input:
sqrt(a+sqrt(b))=sqrt(x1)+sqrt(x2)
Solution:
x1=(a+sqrt(a^2-b))/2
x2=(a-sqrt(a^2-b))/2
by PHPBB12345
June 20th, 2020, 3:08 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

Image
by PHPBB12345
June 17th, 2020, 5:54 pm
Forum: Other Cellular Automata
Topic: NaiveLife Emulated: A reading-order simulation of Life
Replies: 10
Views: 706

Re: NaiveLife Emulated: A reading-order simulation of Life

Redstoneboi wrote:
May 24th, 2020, 9:46 pm

Code: Select all

x = 10, y = 8, rule = NaiveLifeEmulated
D4$6.3A$6.A.A$8.2A$9.A!
Mirrored:

Code: Select all

x = 11, y = 12, rule = NaiveLifeEmulated
D3$6.2A$8.A$7.2A$8.2A2$7.A.A$7.A.2A$8.3A$9.2A!
by PHPBB12345
June 16th, 2020, 11:03 pm
Forum: Other Cellular Automata
Topic: Simple Life(B2k34c/S2-c34z8)
Replies: 20
Views: 810

Re: Simple Life(B2k34c/S2-c34z8)

x = 15, y = 32, rule = B2k34c/S2-c34z8 oo.oo.o.o.oo.oo$ oo.o.oo.oo.o.oo$ ...o...o...o...$ oooo...o...oooo$ o...oo.o.oo...o$ .ooo..o.o..ooo.$ ...o..o.o..o...$ ...oooo.oooo...$ o......o......o$ oooooo.o.oooooo$ ..o..o.o.o..o..$ ....o..o..o....$ ooooo.o.o.ooooo$ o....oo.oo....o$ .ooo...o...ooo.$ ..o.o...
by PHPBB12345
June 15th, 2020, 9:23 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

语文课本《小青蛙》

河水清清天气晴,
小小青蛙大眼睛。
保护禾苗吃害虫,
做了不少好事情。
请你爱护小青蛙,
好让禾苗不生病。
by PHPBB12345
June 4th, 2020, 9:11 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Fractal thread

z' = z-tan(z)+c*sec(z):
Image
by PHPBB12345
June 4th, 2020, 7:25 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

a(1) = floor(cot(1)) = 0 a(2) = floor(cot(cot(1))) = 1 a(3) = floor(cot(cot(cot(1)))) = 0 a(4) = floor(cot(cot(cot(cot(1))))) = 4 a(5) = floor(cot(cot(cot(cot(cot(1)))))) = 0 a(6) = floor(cot(cot(cot(cot(cot(cot(1))))))) = 1 a(7) = floor(cot(cot(cot(cot(cot(cot(cot(1)))))))) = 0 a(8) = floor(cot(cot...
by PHPBB12345
May 27th, 2020, 4:25 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

control group = 对照组
treatment group = 实验组
by PHPBB12345
May 22nd, 2020, 11:14 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

#C lim (x-1)*log(1-x)-(x+1)*log(x+1) = -2 log 2 #C _ #C x->1 #C [[ VIEWONLY ]] x = 702, y = 42, rule = B/S012345678 110bo73bo26bo73bo55bo73bo63bo73bo$109bo75bo24bo75bo53bo75bo61bo75bo$9b 4o51b4o40bo77bo22bo77bo51bo77bo15b4o40bo77bo92b4o$11b2o7bo45b2o40bo12b o64bo22bo66bo10bo51bo66bo10bo17b2o40bo66b...
by PHPBB12345
May 22nd, 2020, 4:13 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Find Last A-sequence

var child_process = require('child_process'); var http = require("http"); var querystring = require("querystring"); var postData = querystring.stringify({ "q":"keyword:allocated|keyword:recycled|keyword:nonn|keyword:sign|keyword:dead", "fmt":"json", }); var options={ hostname: "oeis.org", path: "/s...
by PHPBB12345
May 20th, 2020, 10:23 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Riemann zeta approximation

function zeta_approx (s, i) { var n = s - 1, j = Math.floor(i); var x = Math.pow(j + 0.5, -n) / n; while (j) { x += Math.pow(j, -s); j--; } return x; } function zeta_approx_2 (s) { var x = -9.544466076366965e-18, t = s - 1; x = t * x + 2.1677312200726828e-16; x = t * x - 2.3997862217709992e-15; x =...
by PHPBB12345
May 10th, 2020, 9:59 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

f(x) = f(0) + f'(0) * x + f''(0) / 2 * x^2 + f'''(0) / 6 * x^3 + f''''(0) / 24 * x^4 + O(x^5) f(-x) = f(0) - f'(0) * x + f''(0) / 2 * x^2 - f'''(0) / 6 * x^3 + f''''(0) / 24 * x^4 + O(x^5) (f(x) + f(-x)) / 2 = f(0) + f''(0) / 2 * x^2 + f''''(0) / 24 * x^4 + O(x^6) (f(x) - f(-x)) / 2 = f'(0) * x + f...
by PHPBB12345
May 9th, 2020, 7:19 am
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts

How to "implements" carnot's cycle in reversible cellular automata?
by PHPBB12345
May 2nd, 2020, 5:48 pm
Forum: The Sandbox
Topic: Random posts
Replies: 4951
Views: 555916

Re: Random posts