United States of Voronoi

Рет қаралды 49,503

7 жыл бұрын

Is there a better way to choose US state boundaries? Voronoi diagrams can do the job.
Voronoi Diagrams by Jason Davies:
United States of Voronoi: www.jasondavies.com/maps/voro...
World Airports Voronoi: www.jasondavies.com/maps/voro...
Music: "Daily Beetle" Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 License creativecommons.org/licenses/b...
Street maps by OpenStreetMap contributors. Tiles courtesy of Andy Allan.
Picture of Don Knuth - By Flickr user Jacob Appelbaum, uploaded to en.wikipedia by users BeSherman, Duozmo (Flickr.com (via en.wikipedia)) [CC BY-SA 2.5 (creativecommons.org/licenses/b...)], via Wikimedia Commons
Voronoi diagram - By Balu Ertl (Own work) [CC BY-SA 4.0 (creativecommons.org/licenses/b...)], via Wikimedia Commons
Picture of Beijing National Aquatics Centre - By Morio (Own work) [CC BY-SA 4.0 (creativecommons.org/licenses/b...)], via Wikimedia Commons
Picture of Alibaba headquarters - By HASSELL [CC BY-SA 4.0 (creativecommons.org/licenses/b...)], via Wikimedia Commons
Thiessen Polygons - By Emilio Gomez Fernandez (Own work) [GFDL (www.gnu.org/copyleft/fdl.html) or CC BY-SA 3.0 (creativecommons.org/licenses/b...)], via Wikimedia Commons
Voronoi Fortune Droite Balayage Tangente Cercle - By Cdang (Own work) [CC BY-SA 4.0 (creativecommons.org/licenses/b...)], via Wikimedia Commons
Sound effects obtained from www.zapsplat.com
Sources:
Delaunay triangulation. (2017, July 1). In
Wikipedia, The Free Encyclopedia.
Retrieved from en.wikipedia.org/w/index.php?....
Drysdale, S. (1993, July 19).
Voronoi diagrams: applications from archaeology to zoology.
Retrieved from www.ics.uci.edu/~eppstein/gin....
Kadish, S. (n.d.).
Voronoi map of the USA.
Retreived from vizual-statistix.tumblr.com/po....
Voronoi diagram. (2017, June 19). In
Wikipedia, The Free Encyclopedia.
Retrieved
from
en.wikipedia.org/w/index.php?....

Пікірлер: 61

@BigDBrian 7 жыл бұрын

I think you should've described how a Voronoi diagram is constructed. It's not entirely obvious, though a good starting point seems to be perpendicular bisectors & their crosspoints

@bluewildflower12 7 жыл бұрын

Such an amazing video! I loved the graphics! Everything looked so beautiful.

@AdrianColley 7 жыл бұрын

I love this! I've long thought that fuel stations should be forced to display their own prices and the prices of their Delaunay neighbours, so that the market mechanism will work efficiently.

@candramargarena3431 2 жыл бұрын

This is such a good vids 👍

@christopherlum4736 7 жыл бұрын

I wonder what the world map would look like with this concept.

@unvergebeneid 7 жыл бұрын

I wonder what the South China Sea would look like with this concept...

@TheSucread 7 жыл бұрын

Someone already did exactly this: www.jasondavies.com/maps/voronoi/capitals/

@christopherlum4736 7 жыл бұрын

nice

@youssefmousa2830 7 жыл бұрын

greenland will be... wow. and europe tho

@StarTheTripleDevil 6 жыл бұрын

TheSucread So Finland would be bigger and Sweden would be smaller.

@shellypooper 7 жыл бұрын

This is excellent

@ghosttwo2 7 жыл бұрын

I love this. I wonder if there's a way to generate a similar graph, but with cells of equal area? I can imagine some point layouts that would make this very challenging.

@StarTheTripleDevil 6 жыл бұрын

I remember once thinking about splitting the world like that between me and my 11-14 internet friends at the time and how I would probably have the largest area. Of course, I didn't know about the term "Voronoi" back then.

@bentoth9555 6 жыл бұрын

Voronoi diagrams also helped in what was, basically, the founding of epidemiology. John Snow, a 19th-century doctor, used what was essentially a Voronoi diagram (before Voronoi was even born) to figure out the source of a cholera epidemic in London. He was able to trace it to the communal water pump on Broad Street.

@jamesc6028 7 жыл бұрын

Very interesting

@sams_3d_stuff 5 жыл бұрын

Thank you

@joulesjams20 7 жыл бұрын

I came at the right time that the views and likes share a prime factor. What a time

@joulesjams20 7 жыл бұрын

And the likes itself is a prime

@TheBurningWarrior 5 жыл бұрын

Just using the specific prime factor 2 that should happen 1/4 of the time. The possibilities are: 1 a is even and b is even, 2 a is odd and b is odd, 3 a is odd and b is even, 4 a is even b is odd I conjecture that the odds for any one state in this special case should be the same as any other leading to the 1/4 chance of both being even. For 3 you get the same options substituting having the prime power of 3 but different odds for each option. there is a 1 in 3 chance of a number in a finite and sequentially ordered set of natural numbers being divisible by three, so it should be about 1 in 9 chance of option 1. I'm not a statistician, and I may be going about this wrong, but it seems like (if I'm doing this right) there should be a 1 in p^2 chance of 2 random numbers sharing the prime factor p, so there should be greater than a 44.7 in 100 chance that both should contain a prime less than 100. I did this real quick for a KZfaq comment between doing other things, so, please, if you know what you're doing better than I do, let me know where I went wrong.

@PaulGoux 4 жыл бұрын

rofl, numberphile would love you.

@completeandunabridged.4606 7 жыл бұрын

I really like your videos! Have you ever heard of the sequence known as narayana's cow's? It is similar to the fibonacci sequence (I am not one of those golden ratio worshipers, don't worry) and approaches an interesting term to term ratio.

@completeandunabridged.4606 7 жыл бұрын

1,1,1,2,3,4,6,9,11,17,28...

@maynk7096 2 жыл бұрын

This is so fkin cool

@eamonnsiocain6454 7 жыл бұрын

A Voronoi Algorithm to redraw Congressional Districts on the basis of Population Parity to within .03 SE would make more sense.

@heyandy889 7 жыл бұрын

good shit

@fabiocamporesi3550 Жыл бұрын

What about Alaska and Hawaii?

@aedificabantur 7 жыл бұрын

so how does one construct a Voronoi diagram? for example, given the points (3,13) (-6,4) (0,5) and (-9, -9) how would I determine cell boundaries?

@alexsiemers7898 7 жыл бұрын

Use a computer to do it for you

@joshvictor110 7 жыл бұрын

lol

@inigo8740 6 жыл бұрын

Here is my simple solution: Construct the perpendicular bisectors of the "relevant" connections. The rest is straight forward.

@nugs1951 7 жыл бұрын

So how do actually make the diagram?

@shellypooper 7 жыл бұрын

well naively you could took the bisection of every two points and then you obtain a polygon that seems to work. Now you don't want that because complexity wise it's n², I guess there's a smart way.

@altair-channel 7 жыл бұрын

3:31 When one of your friends lives in Skid Row

@52flyingbicycles 3 жыл бұрын

Ironically, taco stands (and all sorts of businesses) actually set up really close to each other to take as much business for themselves. It actually doesn’t help either of them and makes customers have to travel further, but the social trap leads to them being super close instead of optimally far

@czechthisout 7 жыл бұрын

I'd like to see this with professional sports teams

@ryanmurray5973 7 жыл бұрын

How? Sports teams can move.

@alexsiemers7898 7 жыл бұрын

Well, with their home stadiums/cities.

@abrahamplai7676 3 жыл бұрын

And what about moving the location of capitals given the actual map to fit the same principle, instead of changing the map to fit the capitals?

@TippingPointMath 3 жыл бұрын

You can't have a Voronoi diagram with the existing map. A Voronoi diagram has straight edges as boundaries, obviously not the case with many borders between states.

@PankajKumar-os3tm 3 жыл бұрын

@@TippingPointMath Woah, you have stopped making videos but still replying to some comments

@dmravi13 7 жыл бұрын

hang on im a bit confused... so for 6 friends you say the delauney triangle has 10 sides, but according to your equation 3n-6, i should have 12... am i doing something wrong?

@kresimirnezmah5393 7 жыл бұрын

dmravi13 maybe the formula only works with powers of 10

@HienNguyenHMN 6 жыл бұрын

Use Voronoi diagrams for voting districts.

@Cloiss_ 6 жыл бұрын

This would not work because they are based on area, not population. A better method, albeit more difficult, is the "shortest-line" method, which divides along the shortest line into two equal halves.

@BroadcastBro 7 жыл бұрын

I loved the video! But what a Taco stand owner should do is actually the opposite: he should stay as close as possible to all of his competitors. That's a Game theory concept.

@WAQWBrentwood 7 жыл бұрын

BroadcastBro In the case presented, I believe that it was for a new outlet in a chain reducing competition among outlets in that chain, not reducing competition to rival taco chains or standalone rivals.

@anawesomepet 3 жыл бұрын

Auto generated subtitles at the end: Should we declare the United States Of Foreign Oil?

@NotQuiteFirst 7 жыл бұрын

Wouldn't you just look at the map and see which post office is nearest to your house? It seems like pointless extra work to divide the map into a voronoi diagram just to see which cell your house is in :/

@ryanmurray5973 7 жыл бұрын

But you could then send it to everyone in the city, and everyone will be able to find their nearest post office without as much effort.

@LineOfThy Жыл бұрын

Is reusable

@cloroxbleach9222 6 жыл бұрын

Delaware would still be the insignificant state that it is.

@lr5867 7 жыл бұрын

Upon the inception of the Greater Republic Freedonia this will be implemented.

@yuwish6320 2 жыл бұрын

Interesting. MAssachusetts got screwed. NY got screwed. And Vermont got all of upstate NY and half of NH, giving up only the land south of Rutland. Choice.

@johnabreuolivo8119 2 жыл бұрын

YES! United States of Voronoi is a perfect name, and ... by the way, Voronoi (Georgy Voronoy) was Russian !!! ha - ha -ha -ha

@bravebrowser6358 5 жыл бұрын

brave.com

@mrphillipjohn227 5 жыл бұрын

The USA√3 such cubed "COFFEE" has water agua h"2"o Fifty Contiguous indivisible fresh as salt water connection connected with Thee We' The People Theeself each to also Speech Cook County Alaska Virginia LA ; i