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Super User
Friend and Foe

I'm not sure what the point of this training exercise was, but I did learn Bob's name. There were a bunch of us in a large room and we were each assigned a friend and a foe (secretly, no shared information). We milled about the room, trying to move away from our foe and towards our friend. After a while we stopped and the trainer asked if we had identified the two people that had us as their secret friend/foe. I had not, and I wondered about the folks that claimed they did. Here's a video of JMP running a simulation of the game. There are several color-coded friend loops, and I can see why some people might have easily identified friends. Most everyone is also coded with a circle, but there are two diamond pairs as well; these poor folks have a mutual friend/enemy relationship. You'll also see red and green vector arrows on the points; the red foe vector arrows get short quickly, except on the diamond pairs. The green friend vectors tug the friend groups together.

Probably the most interesting thing in this JSL is the matrix math that gathers info from all the players without an explicit loop. (Near the comment push crowded points apart.)  It moves the current player away from the closest other players by calculating their distances and weighting their vectors by the inverse of the distance. It takes advantage of a division by zero for the current point's distance from itself; the missing value does not change the weighted mean. When you watch the video you can see the points are dodging each other. When you run the JSL, check out the sliders.

``````// Friend & Foe game
nPlayers = 39; // 3 or more required, by 9 there are usually 2 disjoint friend loops.
// tweaked for many players, smaller numbers may need some help passing the tests below.
// also tweaked for 4K images, smaller will be faster, font sizes etc...
//directory = "f:/FriendFoe/Pics/";
//Delete Directory( directory );
//Create Directory( directory );
nIterations = 14000;
result = J( nIterations, 2 * nPlayers/*x-y coords*/, . ); // collect for analysis?

fsize = 950; // fits my screen. tweak as needed.
xyaxisMin = -5;
xyaxisMax = 5;
self = 1 :: nPlayers;
While( 1, // keep trying until additional rules are satisfied
// randomly assign friends and foes until
// no player has the same other player for
// both friend and foe and no player is its
// own friend or foe.
attempts = 0;
While( 1, // keep trying until...
friends = Random Shuffle( self );
foes = Random Shuffle( self );
If( !Any( friends == foes ) & !Any( friends == self ) & !Any( foes == self ),
Break()
);
attempts += 1;
Show( attempts ); // surprisingly, this never gets too bad.
);
dtGame = New Table( "game",
invisible,
addrows( nPlayers ),
New Column( "id", Numeric, "nominal", Set Values( self ) ),
New Column( "x", Numeric, "Continuous", Format( "Best", 6 ), Set Values( J( nPlayers, 1, Random Uniform( -1, 1 ) ) ) ),
New Column( "y", Numeric, "Continuous", Format( "Best", 6 ), Set Values( J( nPlayers, 1, Random Uniform( -1, 1 ) ) ) ),
New Column( "friend", Numeric, "nominal", Set Values( friends ) ),
New Column( "foe", Numeric, "nominal", Set Values( foes ) ),
// needed for the graph's green and red vectors...
New Column( "xfriend", Numeric, "Continuous", Format( "Best", 6 ), Set each Value( 0 ) ),
New Column( "yfriend", Numeric, "Continuous", Format( "Best", 6 ), Set each Value( 0 ) ),
New Column( "xfoe", Numeric, "Continuous", Format( "Best", 6 ), Set each Value( 0 ) ),
New Column( "yfoe", Numeric, "Continuous", Format( "Best", 6 ), Set each Value( 0 ) ),
New Column( "loopid", Numeric, "Continuous", Format( "Best", 6 ), Set each Value( . ) )
);
// color code the friend loops just to make the video pretty
nLoops = 0;
For( irow = 1, irow <= N Rows( dtGame ), irow += 1,
If( Is Missing( dtGame:loopid[irow] ),
nLoops += 1;
// the loop of friends should come back to the start
For( jrow = dtGame:friend[irow], Is Missing( dtGame:loopid[jrow] ), jrow = dtGame:friend[jrow],
dtGame:loopid[jrow] = nLoops;
lastjrow = jrow;
);
If( lastjrow != irow,
Throw( "weird loop" )
);
)
);
// above counted disjoint friend loops
If( nloops >= 4 | nPlayers < 20,
dtGame << Color or Mark by Column( :loopid, Color Theme( "Jet" ), Marker( 0 ) );
For Each Row( dtGame, Row State() = Combine States( Marker State( 12/*8circle*/ ), (Row State()) ) );
paired = 0;
// above set the color and circle marker, now look for the friend-foe pairs and
// set a diamond marker.
For Each( {r}, dtGame << getrowswhere( dtGame:friend[dtGame:foe] == dtGame:id | dtGame:foe[dtGame:friend] == dtGame:id ),
Show( r, (Row State( dtGame, r )) );
paired += 1;
Row State( dtGame, r ) = Combine States( Marker State( 16/*4diamond*/ ), (Row State( dtGame, r )) );

);
Show( paired );
Wait( 0 );
If( paired >= 4 | nPlayers < 6,
Break() // finally! found a set we like.
);
);
Close( dtGame, nosave );
);

New Window( "dance",
pvlb = V List Box(
// extra spacer boxes to force the window to size for the video...un-tweak them is fine
//Spacer Box( size( 4200, 100 ), color( "white" ) ),
hlb = H List Box(
//Spacer Box( size( 20, 2500 ), color( "white" ) ),
vlb = V List Box(),
gb = dtGame << Graph Builder(
Size( fsize, fsize ),
Show Control Panel( 0 ),
Show Legend( 0 ),
Show Title( 0 ),
Show X Axis Title( 0 ),
Show Y Axis Title( 0 ),
Variables( X( :x ), Y( :y ) ),
Elements( Points( X, Y, Legend( 5 ) ) ),
SendToReport(
Dispatch( {}, "Graph Builder", OutlineBox, {Set Title( "" ), Image Export Display( Normal )} ),
Dispatch( {}, "Graph Builder", FrameBox, {Marker Size( 18 )} )
)
),
//ndb = dtGame << newdatabox// add an embedded data table to the display for the video, makes it a bit slower
,
//Spacer Box( size( 10, 2500 ), color( "white" ) )
),
//Spacer Box( size( 4200, 10 ), color( "white" ) )
)
);
try(ndb << Close Side Panels); // tighten up the display by removing the left side panels of the embedded table

temperature = .;

// add the script to the GraphBuilder to show the connections
Report( gb )[framebox( 1 )] << addgraphicsscript(
Local( {irow, friendlength, foelength, myPos, ifriend, ifoe, foepos, friendpos},
friendlength = 0;
foelength = 0;
For( irow = 1, irow <= N Rows( dtGame ), irow += 1, // every row in the table has a connection to a friend and a foe
myPos = dtGame[irow, {x, y}];
myFoeVec = 1000 * Exp( ArrowScale ) * dtGame[irow, {xFoe, yFoe}];
foelen = Sqrt( Sum( myFoeVec ^ 2 ) );
minlen = 0.06; // tune minimum arrow length for dot size
If( foelen < minlen,
myFoeVec *= minlen / foelen
);
myFriendVec = 1000 * Exp( ArrowScale ) * dtGame[irow, {xFriend, yFriend}];
friendlen = Sqrt( Sum( myFriendVec ^ 2 ) );
If( friendlen < minlen,
myFriendVec *= minlen / friendlen
);
ifriend = dtGame:friend[irow];
ifoe = dtGame:foe[irow];
foepos = dtGame[ifoe, {x, y}];
friendpos = dtGame[ifriend, {x, y}];
Transparency( 1 );
foelength += Sqrt( Sum( (mypos - foepos) ^ 2 ) );
Transparency( .2 );
Pen Color( "black" );
Pen Size( 3 );
Line( {mypos[1], mypos[2]}, {foepos[1], foepos[2]} );
Transparency( 1 );
Pen Color( "dark red" );
Pen Size( 7 );
Arrow( {mypos[1], mypos[2]}, {mypos[1] + myFoeVec[1], mypos[2] + myFoeVec[2]} );

friendlength += Sqrt( Sum( (mypos - friendpos) ^ 2 ) );
Transparency( .2 );
Pen Color( "black" );
Pen Size( 3 );
Line( {mypos[1], mypos[2]}, {friendpos[1], friendpos[2]} );
Transparency( 1 );
Pen Color( "dark green" );
Pen Size( 7 );
Arrow( {mypos[1], mypos[2]}, {mypos[1] + myFriendVec[1], mypos[2] + myFriendVec[2]} );

);
Transparency( 1 );
Pen Color( "black" );
Text Color( "black" );
Text(
rightjustified,
{X Origin() + X Range() - X Range() / 20, Y Origin() + Y Range() / 50},
"foe/friend " || Char( foelength / friendlength, 5, 3 )
);
Text( {X Origin() + X Range() / 20, Y Origin() + Y Range() / 50}, "Temperature " || Char( temperature, 7, 2 ) );
)
);

stop = 0;
Report( gb ) << onclose(
stop = 1;
dtGame << setdirty( 0 );
);

step = 0.00001;
PushFoe = Log( 1.0 * step );
PullFriend = Log( 1.0 * step );
PullCenter = Log( 0.1 * step );
PushNearest = Log( 30.0 * step );
ArrowScale = Log( 20 );

vlb << append( H List Box( Text Box( "push foe" ), Slider Box( Log( step * .001 ), Log( step * 50 ), PushFoe ) ) );
vlb << append( H List Box( Text Box( "pull friend" ), Slider Box( Log( step * .001 ), Log( step * 50 ), PullFriend ) ) );
vlb << append( H List Box( Text Box( "pull center" ), Slider Box( Log( step * .001 ), Log( step * 50 ), PullCenter ) ) );
vlb << append( H List Box( Text Box( "push near" ), Slider Box( Log( step * .001 ), Log( step * 5 ), PushNearest ) ) );
vlb << append( H List Box( Text Box( "arrow scale" ), Slider Box( Log( .1 ), Log( 1000 ), ArrowScale ) ) );
Wait( 0.1 );
hlb << maximizewindow;
iteration = 0;
While( !stop & (iteration += 1) <= nIterations,
temperature = Interpolate( // annealing schedule, partially chosen for pretty video
iteration, // high temperature at the beginning makes bigger jumps
0.00 * nIterations, 5000,
0.20 * nIterations, 4000,
0.40 * nIterations, 3000,
0.60 * nIterations, 2000,
0.80 * nIterations, 1000,
1.00 * nIterations, 500
);
oldPos = dtGame[0, {x, y}];
dtGame << Begin Data Update;
For( irow = 1, irow <= N Rows( dtGame ) & !stop, irow += 1,
myPos = oldPos[irow, 0];
foepos = oldPos[dtGame:foe[irow], 0];
friendpos = oldPos[dtGame:friend[irow], 0];
// push crowded points apart...
deltaPos = Repeat( myPos, nPlayers ) - oldPos;
push = 1 / (deltapos[0, 1] ^ 2 + deltapos[0, 2] ^ 2);// closer pushes harder, I'm a missing value.
angles = ATan( deltaPos[0, 2], deltaPos[0, 1] );
deltaPos = temperature * Exp( PushNearest ) * (Mean( Cos( angles ) :* push ) || Mean( Sin( angles ) :* push ));
// pull back to center, more pull far from center
dist = Exp( PullCenter ) * Sqrt( myPos[1] ^ 2 + myPos[2] ^ 2 );
centering = (myPos :* dist);
deltaPos -= temperature * centering;
// move away from foe. push harder when near.
delta = mypos - foepos;
push = 1 / (delta[1] ^ 2 + delta[2] ^ 2);
angle = ATan( delta[2], delta[1] );
foepush = Exp( PushFoe ) * (Cos( angle ) * push || Sin( angle ) * push);
dtGame[irow, {xfoe, yfoe}] = foepush;
deltaPos += temperature * foepush;
// move towards friend. pull harder when far.
delta = mypos - friendpos;
push = Sqrt( delta[1] ^ 2 + delta[2] ^ 2 );
angle = ATan( delta[2], delta[1] );
friendpull = -Exp( PullFriend ) * (Cos( angle ) * push || Sin( angle ) * push);
dtGame[irow, {xfriend, yfriend}] = friendpull;
deltaPos += temperature * friendpull;
// apply the forces...
While( Any( Abs( deltaPos ) > 2 ), deltaPos /= 2 );// limit
dtGame[irow, {x, y}] += deltaPos;
);

dtGame << End Data Update;

If( !stop,
xyrange = Range( dtGame[0, {x, y}] );
xydelta = xyrange[2] - xyrange[1];
targetxymin = xyrange[1] - 3 * xydelta / 100;
xyaxisMin = (99 * xyaxisMin + targetxymin) / 100;
targetxymax = xyrange[2] + 3 * xydelta / 100;
xyaxisMax = (99 * xyaxisMax + targetxymax) / 100;

Report( gb )[framebox( 1 )] << xaxis( {Format( "Fixed Dec", 12, 1 ), Min( xyaxisMin ), Max( xyaxisMax ), Inc( 0.5 )} ) <<
yaxis( {Format( "Fixed Dec", 12, 1 ), Min( xyaxisMin ), Max( xyaxisMax ), Inc( 0.5 )} );
wait(.01);
//		pvlb << savepicture( directory || Right( Char( 1e9 + iteration ), 8 ) || ".png", "png" );
result[iteration, 0] = Shape( dtGame[0, {x, y}], 1, 2 * nPlayers );
);
);
``````

Last Modified: Jan 7, 2024 12:50 AM