Dominion Strategy Forum

Please login or register.

Login with username, password and session length
Pages: 1 ... 39 40 [41] 42 43 ... 201  All

Author Topic: Random Stuff  (Read 1162305 times)

0 Members and 4 Guests are viewing this topic.

Awaclus

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 11808
  • Shuffle iT Username: Awaclus
  • (´。• ω •。`)
  • Respect: +12846
    • View Profile
    • Birds of Necama
Re: Random Stuff
« Reply #1000 on: October 20, 2013, 03:03:07 pm »
+6

Logged
Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

The YouTube channel where I make musicDownload my band's Creative Commons albums for free

qmech

  • Torturer
  • *****
  • Offline Offline
  • Posts: 1918
  • Shuffle iT Username: qmech
  • What year is it?
  • Respect: +2320
    • View Profile
Re: Random Stuff
« Reply #1001 on: October 21, 2013, 03:48:57 am »
+1



The dots are only moving in straight lines.

I finally got around to writing out a mathematical proof that those really are straight lines.

What would it look like if the balls weren't sinusoid-ing back and forth, but instead moved with constant speed?

What if the radius of the inner "circle" were not exactly equal to half that of the outer? How would that affect the paths the balls would take? Some sort of weird cycloid or something?

For different radii you do indeed get a hypocycloid.

If the points move back and forth and constant speed then the boundaries of the shape will look like r=k.theta for some constant k, so you'll get a region bounded by segments of two spirals—in particular, it will have a point at either end.
Logged

Kuildeous

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3840
  • Respect: +2219
    • View Profile
Re: Random Stuff
« Reply #1002 on: October 21, 2013, 08:28:01 am »
+5

I finally got around to writing out a mathematical proof that those really are straight lines.

I must be really lazy, because instead of writing a proof, I just isolated the lines and verified visually that the balls just move back and forth on a straight line.
Logged
A man has no signature

Tables

  • Margrave
  • *****
  • Offline Offline
  • Posts: 2816
  • Build more Bridges in the King's Court!
  • Respect: +3347
    • View Profile
Re: Random Stuff
« Reply #1003 on: October 21, 2013, 08:49:56 am »
+4

I finally got around to writing out a mathematical proof that those really are straight lines.

I must be really lazy, because instead of writing a proof, I just isolated the lines and verified visually that the balls just move back and forth on a straight line.

What you think you said: "You can just do this by eye"

What you actually said: "I am not a mathematician"

:P
Logged
...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.

SirPeebles

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3249
  • Respect: +5459
    • View Profile
Re: Random Stuff
« Reply #1004 on: October 21, 2013, 08:55:03 am »
0

I finally got around to writing out a mathematical proof that those really are straight lines.

I must be really lazy, because instead of writing a proof, I just isolated the lines and verified visually that the balls just move back and forth on a straight line.

Let me rephrase this then.  I verified that they really are rotating around a center which is itself rotating, where each rotation has the same radius and speed, but opposite direction.
Logged
Well you *do* need a signature...

Kirian

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7096
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9411
    • View Profile
Re: Random Stuff
« Reply #1005 on: October 21, 2013, 09:31:09 am »
+1

I finally got around to writing out a mathematical proof that those really are straight lines.

I must be really lazy, because instead of writing a proof, I just isolated the lines and verified visually that the balls just move back and forth on a straight line.

Let me rephrase this then.  I verified that they really are rotating around a center which is itself rotating, where each rotation has the same radius and speed, but opposite direction.

I'm not entirely certain which amuses me more:  the fact that I can also verify this by eye (if you spin the entire figure counterclockwise, the whole thing works like two gears and the inner circle will stay in place), or the fact that I have no idea how proving that also proves that the points are moving along straight lines.
Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

SirPeebles

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3249
  • Respect: +5459
    • View Profile
Re: Random Stuff
« Reply #1006 on: October 21, 2013, 10:20:16 am »
0

I finally got around to writing out a mathematical proof that those really are straight lines.

I must be really lazy, because instead of writing a proof, I just isolated the lines and verified visually that the balls just move back and forth on a straight line.

Let me rephrase this then.  I verified that they really are rotating around a center which is itself rotating, where each rotation has the same radius and speed, but opposite direction.

I'm not entirely certain which amuses me more:  the fact that I can also verify this by eye (if you spin the entire figure counterclockwise, the whole thing works like two gears and the inner circle will stay in place), or the fact that I have no idea how proving that also proves that the points are moving along straight lines.

I don't mean that it proves that they move in straight lines.  This animated image is sort of like an optical illusion, but not really.  There is not an apparent contradiction involved, but rather a coincidence.  At least for me, my mind sees the circular motion immediately, and it is only with the visual aid of the beads on rods that I see the linear motion.  The coincidence that both are occurring simultaneously is unexpected and jarring.  The resolution that I was looking for, then, is either a proof that the circular motion results in the linear motion, or that the linear motion results in the circular motion.
Logged
Well you *do* need a signature...

Thisisnotasmile

  • Saboteur
  • *****
  • Offline Offline
  • Posts: 1493
  • Respect: +676
    • View Profile
Re: Random Stuff
« Reply #1007 on: October 21, 2013, 12:45:03 pm »
+4

The '60s called...

Logged

qmech

  • Torturer
  • *****
  • Offline Offline
  • Posts: 1918
  • Shuffle iT Username: qmech
  • What year is it?
  • Respect: +2320
    • View Profile
Re: Random Stuff
« Reply #1008 on: October 21, 2013, 01:16:54 pm »
0

I don't mean that it proves that they move in straight lines.  This animated image is sort of like an optical illusion, but not really.  There is not an apparent contradiction involved, but rather a coincidence.  At least for me, my mind sees the circular motion immediately, and it is only with the visual aid of the beads on rods that I see the linear motion.  The coincidence that both are occurring simultaneously is unexpected and jarring.  The resolution that I was looking for, then, is either a proof that the circular motion results in the linear motion, or that the linear motion results in the circular motion.

When I look at it I see a circle rotating and the intersections of the circle with the (fixed) lines highlighted.  It's as if the circle is made of light and rotating behind a disc with radial slits in—the dots are the bright points where the light shines through.  In that model there isn't any straight line motion to be explained.
Logged

SirPeebles

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3249
  • Respect: +5459
    • View Profile
Re: Random Stuff
« Reply #1009 on: October 21, 2013, 01:22:15 pm »
0

I don't mean that it proves that they move in straight lines.  This animated image is sort of like an optical illusion, but not really.  There is not an apparent contradiction involved, but rather a coincidence.  At least for me, my mind sees the circular motion immediately, and it is only with the visual aid of the beads on rods that I see the linear motion.  The coincidence that both are occurring simultaneously is unexpected and jarring.  The resolution that I was looking for, then, is either a proof that the circular motion results in the linear motion, or that the linear motion results in the circular motion.

When I look at it I see a circle rotating and the intersections of the circle with the (fixed) lines highlighted.  It's as if the circle is made of light and rotating behind a disc with radial slits in—the dots are the bright points where the light shines through.  In that model there isn't any straight line motion to be explained.

Let's imagine that there is a big blue dot right in the middle of the "circle" of white dots.  Then in your model it is clear that the blue dot moves in a circle and that the white dots move on straight lines.  What isn't immediately clear is the emergent behavior that the white dots rotate around the blue dot.  That circular motion is not obvious until you see the animation (or carefully analyze some equations).
Logged
Well you *do* need a signature...

Ozle

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3625
  • Sorry, this text is personal.
  • Respect: +3360
    • View Profile
Re: Random Stuff
« Reply #1010 on: October 21, 2013, 01:45:12 pm »
0

The '60s called...



Why did they never combine this with an Etch a Sketch I wonder..
Logged
Try the Ozle Google Map Challenge!
http://forum.dominionstrategy.com/index.php?topic=7466.0

Sullying players Enjoyment of Innovation since 2013 Apparently!

qmech

  • Torturer
  • *****
  • Offline Offline
  • Posts: 1918
  • Shuffle iT Username: qmech
  • What year is it?
  • Respect: +2320
    • View Profile
Re: Random Stuff
« Reply #1011 on: October 21, 2013, 01:47:50 pm »
+1

Let's imagine that there is a big blue dot right in the middle of the "circle" of white dots.  Then in your model it is clear that the blue dot moves in a circle and that the white dots move on straight lines.  What isn't immediately clear is the emergent behavior that the white dots rotate around the blue dot.  That circular motion is not obvious until you see the animation (or carefully analyze some equations).

Yes.  I found the difference in perspective interesting.
Logged

Dsell

  • Saboteur
  • *****
  • Offline Offline
  • Posts: 1290
  • He/Him
  • Respect: +932
    • View Profile
Re: Random Stuff
« Reply #1012 on: October 21, 2013, 11:24:51 pm »
0

Logged
"Quiet you, you'll lynch Dsell when I'm good and ready" - Insomniac


Winner of Forum Survivor Season 2!

sudgy

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3431
  • Shuffle iT Username: sudgy
  • It's pronounced "SOO-jee"
  • Respect: +2706
    • View Profile
Logged
If you're wondering what my avatar is, watch this.

Check out my logic puzzle blog!

   Quote from: sudgy on June 31, 2011, 11:47:46 pm

eHalcyon

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 8689
  • Respect: +9187
    • View Profile
Re: Random Stuff
« Reply #1014 on: October 22, 2013, 09:55:52 pm »
+9



Here's another image of linearly moving dots.
Logged

Kirian

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7096
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9411
    • View Profile
Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

heron

  • Saboteur
  • *****
  • Offline Offline
  • Posts: 1055
  • Shuffle iT Username: heron
  • Respect: +1183
    • View Profile
Re: Random Stuff
« Reply #1016 on: October 23, 2013, 08:12:25 pm »
+1

Here's another image of linearly moving dots.

Somewhat humorously, when I first saw that image I saw that the dots moved in lines, but it took ~15 seconds to see the pattern.
Logged

eHalcyon

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 8689
  • Respect: +9187
    • View Profile
Re: Random Stuff
« Reply #1017 on: October 23, 2013, 08:14:48 pm »
0

Here's another image of linearly moving dots.

Somewhat humorously, when I first saw that image I saw that the dots moved in lines, but it took ~15 seconds to see the pattern.

Are you at all colour blind?  I imagine that the colour really helps with the illusion, so being even partially colour blind might weaken the effect.
Logged

heron

  • Saboteur
  • *****
  • Offline Offline
  • Posts: 1055
  • Shuffle iT Username: heron
  • Respect: +1183
    • View Profile
Re: Random Stuff
« Reply #1018 on: October 23, 2013, 10:44:09 pm »
0

Here's another image of linearly moving dots.

Somewhat humorously, when I first saw that image I saw that the dots moved in lines, but it took ~15 seconds to see the pattern.

Are you at all colour blind?  I imagine that the colour really helps with the illusion, so being even partially colour blind might weaken the effect.
Maybe a tiny bit? My wikipediaing brought up the ishihara color blindness test, which I had no problems with. However, on the red-green test images, I could see the numbers that should be seen if I have red-green color blindness, they were just less contrasted than the normal vision ones.
Additionally, I seem to perceive the boundary between pink and red differently than most people.
Edit: Oh, and if you remember that hue ordering test that someone here posted a while back (you can find it with google) I only got 4 wrong on that.
« Last Edit: October 23, 2013, 10:46:10 pm by heron »
Logged

sudgy

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3431
  • Shuffle iT Username: sudgy
  • It's pronounced "SOO-jee"
  • Respect: +2706
    • View Profile
Re: Random Stuff
« Reply #1019 on: October 24, 2013, 01:16:09 am »
0

Here's another image of linearly moving dots.

Somewhat humorously, when I first saw that image I saw that the dots moved in lines, but it took ~15 seconds to see the pattern.

Me too, but not 15 seconds.  I think it was more, "STRAIGHT LINES!  MUST FIND THEM!"
Logged
If you're wondering what my avatar is, watch this.

Check out my logic puzzle blog!

   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Awaclus

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 11808
  • Shuffle iT Username: Awaclus
  • (´。• ω •。`)
  • Respect: +12846
    • View Profile
    • Birds of Necama
Re: Random Stuff
« Reply #1020 on: October 24, 2013, 01:35:09 am »
+1

It took me a while before I saw the pattern, too. I'm not sure how many seconds it was, but maybe around 5-10.

I'm not colorblind.
Logged
Bomb, Cannon, and many of the Gunpowder cards can strongly effect gameplay, particularly in a destructive way

The YouTube channel where I make musicDownload my band's Creative Commons albums for free

Kirian

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7096
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9411
    • View Profile
Re: Random Stuff
« Reply #1021 on: October 24, 2013, 08:22:38 am »
+1

A sine wave is the projection of a point rotating in a circle onto a straight line.  Film at eleven.
Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

sudgy

  • Cartographer
  • *****
  • Offline Offline
  • Posts: 3431
  • Shuffle iT Username: sudgy
  • It's pronounced "SOO-jee"
  • Respect: +2706
    • View Profile
Re: Random Stuff
« Reply #1022 on: October 25, 2013, 02:34:02 pm »
0

Old McDonald had a farm, E-I-E-I-O
And on that farm he had a fox...
Logged
If you're wondering what my avatar is, watch this.

Check out my logic puzzle blog!

   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Kirian

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7096
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9411
    • View Profile
Re: Random Stuff
« Reply #1023 on: October 25, 2013, 02:53:08 pm »
0

There has to be a market out there for a Candy Box or Cookie Clicker style game, but with beer.
Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

shraeye

  • Minion
  • *****
  • Offline Offline
  • Posts: 690
  • Shuffle iT Username: shraeye
  • More Graph Theory please
  • Respect: +299
    • View Profile
Re: Random Stuff
« Reply #1024 on: October 25, 2013, 03:54:12 pm »
+1

I am the best at that game.  It's called Friday Night.  I play it every friday night, and usually other nights as well.
Logged
Pages: 1 ... 39 40 [41] 42 43 ... 201  All
 

Page created in 0.059 seconds with 21 queries.