Perfect illustration of why chaotic systems are impossible to predict - a miniscule difference in starting conditions and the states diverge dramatically in a short time.
Yes and this is why forecasting the specifics of weather more than a few days is not easy.
Differential equations derived using Lagrangian mechanics in MATLAB's Symbolic Math Toolbox and solved numerically using ode45. The lower segment of the blue pendulum on the right has an initial angle 0.001 radians (~0.057 degrees) greater than the same segment on the red pendulum.
Which is why people on MSNBC yelling at each other over stocks is merely entertainment at best.
oooh This is going to be like one of those mildly satisfying posts where it's all nice and symmetrical. Yes, perfect loop ... Oh god. No. Not that way. Abort. ABORT. JESUS IT'S A MESS AAAAAA
Double pendulum is an example of chaotic behaviour - it has a very strong sensitivity to initial conditions - change them just slightly and its behaviour completely changes.
Tools used: python, numpy, matplotlib
Source: randomly created initial conditions
If you want to see more, you can follow my Twitter bot which posts gifs (every couple of hours) of pendulum motion released from random initial positions.
To all people asking for a source code - I still need to finish/add/improve some more stuff. I hope to release in on my Github profile in about one week time.
I want it to go for longer. 10 hours would be good
To me, there's a certain satisfying feature in all the asymmetry.
The best kind of correct
This the same bitcoin that my friend was 'mining' on his computer 10 years ago?
I should check in and see how he's doing these days
Eh you probably would have sold long before it was worth this much anyway. Don't beat yourself up over it.
Yeah. I'm really regretting downloading everything but getting frustrated and going to bed and never actually going back to make it work.
Everyone forgets this.
My friends talked me out of buying coins when they were like 16c-36c each but other friends who did buy coins all sold when they hit $200 because you were crazy not to.
The lucky people are the ones who bought them and just forgot they had them.
Is it possible to generate one of these from any other point in the map as well?
A cool meta-post would be to repeat for every point on the map and only draw some kind of heat map for how often each point appears with each iteration.
As a Detroiter who has visited Toronto multiple times, I can assure you that driving through Toronto is still significantly faster than driving through Lake Erie.
It'd be cool see the optimal road map for getting to every major city, if we were to rebuild the entire US interstate system.
edit: For all those people who keep saying the same thing. I mean if we were to rebuild all the roads. OR, instead of rebuilding the roads, maybe it'd be more realistic to map the most efficient map for Elon's Hyperloop to reach all the major cities in US. Lets say any city that in the greater metropolitan area has over 500k people.
Congratulations, OP! Also look out - your x-intercept is in ~1.56 years. Don't want to go negative!
I was 19 when I finished basic training for the AF. I weighed exactly 181 lbs, and it was the best shape I had ever been in. You lost an entire Airman, in a year. That is truly amazing.
It’s hard to say how much weight I gained on the trip, especially when you consider what constitutes weight gain. It’s my belief that almost all of the weight I gained was due to water weight (between the car rides and all the restaurant meals). The fact that I went right back to the trend line in a matter of days leads me to believe that I didn’t truly gain or lose anything!
As for pictures, I’m still considering it. If enough people are curious for before/afters, I can provide.
If it were a linear process, then it would have an X intercept at that point. However, the rate of weight loss is proportional to the difference between calories consumed and calories burned, and calories burned is (more or less) a function of body mass.
dW/dt = (c-rW)
W = body weight
c = calories consumed per day (assuming constant and limited by the surgery)
r = constant having to do with metabolism and body composition. r must be positive because the more body mass you have to keep warm, the faster you burn calories.
We can see a couple of things from looking at this equation. One is that weight will be steady when dW/dt = 0 = c-rW, or when W = c/r. Since c/r is a positive divided by a positive, we see there is a positive value for W at which he will maintain his weight.
The other thing to notice is that this differential equation is autonomous, meaning the time variable t does not appear on the right hand side of the equation. Solutions to autonomous systems of differential equations cannot cross, so if he starts weighing more than c/r, he can never weigh less.
Of course, this model doesn't capture everything about a person's weight. He can reduce c by eating even less through will power, or even increase c over baseline by maximizing calories/volume of food by chugging olive oil or stretching what remains of his stomach. Also, r is not technically a constant. The Katch-McArdle formula supposes that r is proportional to lean body mass only, and even then it does not take into account exercise. Nevertheless, we do not need to worry about him wasting away to nothing due to an x-intercept.
Yes, I know you were joking. I just like math.
This is a line graph showing how far the longest east-west interstate highways drift north and south as they travel across the U.S. Each interstate was traced from Google Maps and turned into a line for the graph, so if there's any projection issues blame them.
Edit: These are highways in the Eisenhower Interstate System only, which are the ones with the blue shield like in the graph.
There is a lot of trash on this subreddit. This isn’t one of them, this is excellent. Clear, concise, and the north/south Y axis is a lot of fun. Nice work
That's not part of the Dwight D Eisenhower Interstate Highway system, it's a US Highway. Yes, it's an interstate highway, but it's not an Interstate Highway.
https://en.wikipedia.org/wiki/Interstate_Highway_System which are 4 lane limited access highways the whole way.
https://en.wikipedia.org/wiki/United_States_Numbered_Highway_System Which are often 2 lane and go through cities and towns
P.S. For a stark reference on the difference, you might want to refer to the movie "Cars"
The fun part is a lot of the interstates in both graphs end up in St. Louis, MO. 55, 64, 70, 44 all run right through the city.
I can't believe people go whole days without taking a dump.
I recorded my data on the go in the notes app on my iPhone and then would transfer it to Excel at the end of each month. There’s probably an easier way to do this, like creating a Google form, but if worked for 2017! Hope to improve in 2018.
Data source: my butt
You are so full of shit, and I don't believe you.
Sometimes you just dont gotta go
r/MapsWithoutNZ would like a word with you.
Some might try to argue that the fact New Zealand is literally surrounded by ocean with no borders to list makes it an entirely pointless addition. Those people are monsters who don't understand the importance of this issue. It's the principle of the matter!
Boarders are hard, and this map clearly required a lot of choices and assumptions, but I really like it! Thanks for posting OP!
Fun fact: The Norwegian border with Russia is based of the deepest part of a river. Because of the river eroding the ground Norway gets a couple of inches in Russia every year
It really is spelled "border," like the OP did it.