You can't define it without the Lambert W function, which is defined as the inverse function to the function that sends x to xe^x. The you can describe that curve by y = W(log(x)/x)x/log(x). (The logarithms are base e, naturally.)muzik wrote:What is the equation of the curve present in x^y=y^x?
Things You've Been Doing Other Than CGoL
Re: Things You've Been Doing Other Than CGoL
Re: Things You've Been Doing Other Than CGoL
That would be y = W(ln(x)/x)x/ln(x).Macbi wrote:You can't define it without the Lambert W function, which is defined as the inverse function to the function that sends x to xe^x. The you can describe that curve by y = W(log(x)/x)x/log(x). (The logarithms are base e, naturally.)muzik wrote:What is the equation of the curve present in x^y=y^x?
Re: Things You've Been Doing Other Than CGoL
Most mathematicians I know use "log" to mean base e (or base 2 in information theory or computer science). Using "log" to mean base 10 is uncool because 10 is just an arbitrary number with no mathematical significance. So I avoid using "ln" because if I did use it I'd be worried that people would think that I had deliberately avoided using "log", and that therefore I must be the uncool kind of person who thinks that "log" means base 10.wwei23 wrote:That would be y = W(ln(x)/x)x/ln(x).Macbi wrote:You can't define it without the Lambert W function, which is defined as the inverse function to the function that sends x to xe^x. The you can describe that curve by y = W(log(x)/x)x/log(x). (The logarithms are base e, naturally.)muzik wrote:What is the equation of the curve present in x^y=y^x?
 Goldtiger997
 Posts: 590
 Joined: June 21st, 2016, 8:00 am
Re: Things You've Been Doing Other Than CGoL
I managed to solve a rubik's cube in my left hand while simultaneously juggling two balls in my right hand. It took 2 minutes and 31 seconds. That was after about 15 tries.
Has any one else tried something like this before, or at least attempted to perform two skills/hobbies at once? Another one I recently did was fold a fairly neat paper crane in my left hand while juggling two balls in my right.
Next, I need to try doing it juggling rubik's cubes not balls, or with a 4x4 (I doubt that one)
Has any one else tried something like this before, or at least attempted to perform two skills/hobbies at once? Another one I recently did was fold a fairly neat paper crane in my left hand while juggling two balls in my right.
Next, I need to try doing it juggling rubik's cubes not balls, or with a 4x4 (I doubt that one)

 Posts: 796
 Joined: May 30th, 2016, 8:47 pm
 Location: Milky Way Galaxy: Planet Earth
Re: Things You've Been Doing Other Than CGoL
How about solving the Rubik's cube while juggling it?Goldtiger997 wrote:Next, I need to try doing it juggling rubik's cubes not balls, or with a 4x4 (I doubt that one)
Code: Select all
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
 Majestas32
 Posts: 524
 Joined: November 20th, 2017, 12:22 pm
 Location: 'Merica
Re: Things You've Been Doing Other Than CGoL
...but ln has 2 letters while log has 3...
Please, stop spam searching Snowflakes.
Re: Things You've Been Doing Other Than CGoL
There's some very recent prior art. Que Jianyu solved three 3x3 cubes while juggling them, in just over five minutes.Gamedziner wrote:How about solving the Rubik's cube while juggling it?Goldtiger997 wrote:Next, I need to try doing it juggling rubik's cubes not balls, or with a 4x4 (I doubt that one) :D
At the latest Gathering for Gardner I saw people solving cubes blindfolded, solving them with just their feet, and so on, but I didn't see any cube jugglers... I can juggle, and I can solve Rubik's Cubes, but I must say I'm not too tempted to try combining the two.
 Saka
 Posts: 3206
 Joined: June 19th, 2015, 8:50 pm
 Location: In the kingdom of Sultan Hamengkubuwono X
 Contact:
Re: Things You've Been Doing Other Than CGoL
I've recently been getting into esolangs and I made this:
https://github.com/saka29/TPPLInterpreter
https://github.com/saka29/TPPLInterpreter
Code: Select all
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
 gameoflifemaniac
 Posts: 923
 Joined: January 22nd, 2017, 11:17 am
 Location: There too
Re: Things You've Been Doing Other Than CGoL
Right now there's a total lunar eclipse in Poland. But the clouds are hiding the moon and I'm missing something that happens once in a lifetime.
EDIT: It's over. Now it's visible, but only partial
EDIT: It's over. Now it's visible, but only partial
This is a signature
Re: Things You've Been Doing Other Than CGoL
I don't get to see it at all, the moon will be under the horizon the entire time.gameoflifemaniac wrote:Right now there's a total lunar eclipse in Poland. But the clouds are hiding the moon and I'm missing something that happens once in a lifetime.
EDIT: It's over. Now it's visible, but only partial
Re: Things You've Been Doing Other Than CGoL
Luckily, lunar eclipses aren't really "once in a lifetime", more "once in a few years".gameoflifemaniac wrote:Right now there's a total lunar eclipse in Poland. But the clouds are hiding the moon and I'm missing something that happens once in a lifetime.
EDIT: It's over. Now it's visible, but only partial