def replot_out_dots( radius, thetaRads, X, Y, params ):
# Determine who's out of range
if ( params['displayRegion'] == 'ring' ):
outField = (radius >= params['outerRadiusUnits'])
inField = (radius <= 0)
out = outField + inField
elif ( params['displayRegion'] == 'rect' ):
gtMaxX = (X >= params['maxXunits'])
ltMinX = (X <= params['minXunits'])
gtMaxY = (Y >= params['maxYunits'])
ltMinY = (Y >= params['minYunits'])
outX = ( gtMaxX | ltMinX )
outY = ( gtMaxY | gtMaxY )
out = ( outX | outY )
else:
print "Invalid displayRegion"
if params['debugMode']:
print 'Out= ' + str( sum( outField ) ) + '| In= ' + str( sum( inField ) )+ ' | MaxX = ' + str( numpy.max( X ) ) + ' | MinX = ' + str( numpy.min( X ) ) + ' | MinR = ' + str( numpy.min(radius) )
# Replot based on replotMode and moveMode
if params['replotMode'] == 'wrap':
if params['displayRegion'] == 'ring':
if (params['moveMode'] == 'radial') or (params['moveMode'] == 'rotation') or (params['moveMode'] == 'random'):
if out.any:
radius = numpy.mod( radius, params['outerRadiusUnits'] )
X, Y = pol2cart( thetaRads, radius, units='rads' )
elif (params['moveMode'] == 'laminar'):
if out.any: # mirror reverse X, Y coordinates
X[ out ] = -1.0*X[out]
Y[ out ] = -1.0*Y[out]
thetaRads, radius = cart2pol( X, Y, units='rad' )
elif params['replotMode'] == 'replot-scaled-polar':
if outField.any:
radius[outField], thetaRads[outField], X[outField], Y[outField] = make_dots( sum( outField ), params, min=0., max = params['innerRadiusUnits'], distributionMode = 'scaled-polar' )
if inField.any:
radius[inField], thetaRads[inField], X[inField], Y[inField] = make_dots( sum( inField ), params, min=params['outerRadiusUnits'], max=params['outerRadiusUnits']+params['dotSpeedUnits'], distributionMode = 'scaled-polar' )
elif params['replotMode'] == 'replot-radial':
if out.any:
radius[out], thetaRads[out], X[out], Y[out] = make_dots( sum( out ), params, min=0, max=params['outerRadiusUnits'], distributionMode = 'uniform-polar' )
elif params['replotMode'] == 'replot-rect':
if out.any:
radius[out], thetaRads[out], X[out], Y[out] = make_dots( sum( out ), params, min=params['xMinUnits'], max=params['xMaxUnits'], distributionMode='uniform-rect' )
# Convert changed X,Y to polar
thetaRads, radius = cart2pol( X, Y, units='rad' )
# end if replotMode
return radius, thetaRads, X, Y
def dots_update(dotsX,
dotsY,
frameCount,
dotSpeed=dotSpeed,
frameDeathAfter=np.inf):
# convert to polar coordinates
dotsTheta, dotsRadius = cart2pol(dotsX, dotsY)
# update radius
dotsRadius = (dotsRadius + dotSpeed)
# decide which dots die
lgcOutFieldDots = np.zeros(len(dotsTheta), dtype='bool')
if dotSpeed > 0:
# create lgc for elems where radius too large
lgcOutFieldDots = (dotsRadius >= FieldSizeRadius)
elif dotSpeed < 0:
# create lgc for elems where radius too small
lgcOutFieldDots = (dotsRadius <= innerBorder)
# create logical for where frameCount too high
lgcFrameDeath = (frameCount >= frameDeathAfter)
# combine logicals
lgcDeath = np.logical_or(lgcOutFieldDots, lgcFrameDeath)
# replace dead dots
dotsRadius[lgcDeath] = np.random.uniform(innerBorder,
FieldSizeRadius,
size=sum(lgcDeath))
dotsTheta[lgcDeath] = np.random.rand(sum(lgcDeath)) * 360
# convert
dotsX, dotsY = pol2cart(dotsTheta, dotsRadius)
# increase frameCount for every elements
frameCount += 1
# set the counter for newborn dots to zero
frameCount[lgcDeath] = 0
return dotsX, dotsY, frameCount
def computeChaosPos(dir=0):
if dir == -1: # left
directionRange1 = [-180, -20]
directionRange2 = [20, 180]
elif dir == 1: # right
directionRange1 = [-160, 0]
directionRange2 = [0, 160]
# Initial parameters
dotsTheta = np.random.rand(nDots) * 360 # deg
dotsRadius = (np.random.rand(nDots) ** 0.5) * fieldRadius # in deg
dotsX, dotsY = pol2cart(dotsTheta, dotsRadius) # in deg
XYpos = np.empty((nDots, 2, maxFrames))
for iFrame in range(maxFrames):
# choose direction
dir1 = np.random.rand(int(nDots / 2)) * (directionRange1[1] - directionRange1[0]) + directionRange1[0]
dir2 = np.random.rand(int(nDots / 2)) * (directionRange2[1] - directionRange2[0]) + directionRange2[0]
dirAll = np.hstack((dir1, dir2))
# update position
dotsX, dotsY = dotsX + speedFrame * np.cos(dirAll), dotsY + speedFrame * np.sin(dirAll)
# convert catesian to polar
dotsTheta, dotsRadius = cart2pol(dotsX, dotsY)
outFieldDots = (dotsRadius > fieldRadius) # judge dots outside
if outFieldDots.any():
dotsRadius[outFieldDots] = np.random.rand(sum(outFieldDots)) * fieldRadius
dotsTheta[outFieldDots] = np.random.rand(sum(outFieldDots)) * 360 # deg
dotsX, dotsY = pol2cart(dotsTheta, dotsRadius)
XYpos[:, 0, iFrame] = dotsX
XYpos[:, 1, iFrame] = dotsY
return XYpos
def makeCoherentOris(XYs, coherence, formAngle):
nNew = XYs.shape[0] # length along the first dimension
newOris = random(nNew) * 180 # create a random array 0:180
# select some elements to be coherent
possibleIndices = range(nNew) # create an array of indices...
shuffle(possibleIndices) # ...shuffle it'in-place' (without creating a new array)...
coherentIndices = possibleIndices[0 : int(nNew * coherence)] # ...and take first nnn elements
# set the ori of the coherent elements
theta, radius = cart2pol(XYs[:, 0], XYs[:, 1]) # get polar coordinates for elements
newOris[coherentIndices] = theta[coherentIndices] + formAngle
return newOris
def makeCoherentOris(XYs, coherence, formAngle):
nNew = XYs.shape[0]#length along the first dimension
newOris = random(nNew)*180 #create a random array 0:180
#select some elements to be coherent
possibleIndices = range(nNew)#create an array of indices...
shuffle(possibleIndices) #...shuffle it'in-place' (without creating a new array)...
coherentIndices = possibleIndices[0:int(nNew*coherence)]#...and take first nnn elements
#set the ori of the coherent elements
theta, radius = cart2pol(XYs[:,0], XYs[:,1]) #get polar coordinates for elements
newOris[coherentIndices] = formAngle-theta[coherentIndices]
return newOris
def dots_update_outward(dotsXout, dotsYout):
# convert to polar coordinates
dotsTheta, dotsRadius = cart2pol(dotsXout, dotsYout)
#update radius
dotsRadius = (dotsRadius + dotSpeed)
#random radius where radius too large
outFieldDots = (dotsRadius >= FieldSizeRadius)
dotsRadius[outFieldDots] = np.random.rand(
sum(outFieldDots)) * FieldSizeRadius
# convert
dotsXout, dotsYout = pol2cart(dotsTheta, dotsRadius)
return dotsXout, dotsYout
def dots_update_inward(dotsXin, dotsYin):
# convert to polar coordinates
dotsTheta, dotsRadius = cart2pol(dotsXin, dotsYin)
# update radius
dotsRadius = (dotsRadius - dotSpeed)
# random radius where radius too large
outFieldDots = (dotsRadius <= 0)
dotsRadius[outFieldDots] = (np.random.rand(sum(outFieldDots))**
0.5) * FieldSizeRadius
# convert
dotsXin, dotsYin = pol2cart(dotsTheta, dotsRadius)
return dotsXin, dotsYin
def dots_update_lifetime(dotsX,
dotsY,
frameCount,
dotSpeed=dotSpeed,
frameDeathAfter=np.inf):
# convert to polar coordinates
dotsTheta, dotsRadius = cart2pol(dotsX, dotsY)
# update radius
dotsRadius = (dotsRadius + dotSpeed)
# update frameCount
frameCount += 1
# prepare array for dots that will die from falling out
lgcOutFieldDots = np.zeros(len(dotsTheta), dtype='bool')
# decide which dots fall out during expansion
if dotSpeed > 0:
# create lgc for elems where radius too large (expansion)
lgcOutFieldDots = (dotsRadius >= FieldSizeRadius)
# decide which dots fall out during contraction
elif dotSpeed < 0:
# create lgc for elems where radius too small (contraction)
lgcOutFieldDots = (dotsRadius <= innerBorder)
# decide which dots will die because they got too old
lgcFrameDeath = (frameCount >= frameDeathAfter)
# combine logicals from dots that died due to fell out and high age
lgcDeath = np.logical_or(lgcOutFieldDots, lgcFrameDeath)
radiOffset.append(dotsRadius[lgcDeath])
# calculate new radius for dots that died
dotsRadius[lgcDeath] = np.sqrt(
(np.square(FieldSizeRadius) - np.square(innerBorder)) *
np.random.rand(sum(lgcDeath)) + np.square(innerBorder))
radiOnset.append(dotsRadius[lgcDeath])
# calculate new angle for all dots that died (from age or falling)
dotsTheta[lgcDeath] = np.random.uniform(0, 360, sum(lgcDeath))
# reset the counter for newborn dots that died of high age
frameCount[lgcFrameDeath] = 0
# reset the counter for newborn dots that died from falling out
frameCount[lgcOutFieldDots] = np.random.uniform(
0, dotLife, size=sum(lgcOutFieldDots)).astype(int)
radiDensity.append(dotsRadius)
# convert from polar to Cartesian
dotsX, dotsY = pol2cart(dotsTheta, dotsRadius)
return dotsX, dotsY, frameCount
def make_dots( nDots, params, min=-1, max=1, distributionMode='uniform-rect' ):
if distributionMode == 'scaled-polar': # Adjusts for density change due to outward radial motion
r = numpy.random.rand(nDots)**(0.5)*(max - min) + min
th = numpy.random.rand(nDots)*(2*numpy.pi)-numpy.pi
X, Y = pol2cart( th, r, units='rad' )
elif distributionMode == 'uniform-polar':
r = numpy.random.rand(nDots)*(max - min) + min
th = numpy.random.rand(nDots)*(2*numpy.pi)-numpy.pi
X, Y = pol2cart( th, r, units='rad' )
elif distributionMode == 'fixed-circle':
th = numpy.random.rand(nDots)*(2*numpy.pi)-numpy.pi
r = numpy.ones(nDots)*.95
X, Y = pol2cart( th, r, units='rad' )
elif distributionMode == 'hybrid-uniform-rect-polar': # dots of uniform density in circular region
X, Y = numpy.random.rand(nDots)*(max-min)+min, numpy.random.rand(nDots)*(max-min)+min
th, r = cart2pol( X, Y, units = 'rad' )
outR = ( r >= params['outerRadiusUnits'] )
r[ outR ] = numpy.random.rand(sum(outR))*params['outerRadiusUnits']
X, Y = pol2cart( th, r, units='rad' )
else : # default is random in [-1,1] and [-1,1] in Cartesian coordinates
X, Y = numpy.random.rand( nDots )*(max - min) + min, numpy.random.rand( nDots )*(max - min) + min
th, r = cart2pol( X, Y, units = 'rad' )
return r, th, X, Y
def makeCoherentOris(XYs, coherence, formAngle):
# length along the first dimension:
nNew = XYs.shape[0]
# random orientations:
newOris = random(nNew) * 180
# select some elements to be coherent
possibleIndices = list(range(nNew)) # create an array of indices
shuffle(possibleIndices) # shuffle it 'in-place' (no new array)
coherentIndices = possibleIndices[0:int(nNew * coherence)]
# use polar coordinates; set the ori of the coherent elements
theta, radius = cart2pol(XYs[:, 0], XYs[:, 1])
newOris[coherentIndices] = formAngle - theta[coherentIndices]
return newOris
def makeCoherentOris(XYs, coherence, formAngle):
# length along the first dimension:
nNew = XYs.shape[0]
# random orientations:
newOris = random(nNew) * 180
# select some elements to be coherent
possibleIndices = list(range(nNew)) # create an array of indices
shuffle(possibleIndices) # shuffle it 'in-place' (no new array)
coherentIndices = possibleIndices[0: int(nNew * coherence)]
# use polar coordinates; set the ori of the coherent elements
theta, radius = cart2pol(XYs[: , 0], XYs[: , 1])
newOris[coherentIndices] = formAngle - theta[coherentIndices]
return newOris
def move_dots( r, th, X, Y, params ):
if params['moveMode'] == 'radial':
# Coherent
r[ params['cohIndex'] ] += params['dotSpeedUnits']
X[ params['cohIndex'] ], Y[ params['cohIndex'] ] = pol2cart(th[ params['cohIndex'] ], r[ params['cohIndex'] ], units='rad')
# Incoherent
if params['nDots'] > params['nCoherent']:
inCohIndex = numpy.invert( params['cohIndex'] )
dTheta = numpy.random.rand(params['nDots']-params['nCoherent'])*numpy.pi*2.0
X[ inCohIndex ] += params['dotSpeedUnits']*numpy.cos( dTheta )
Y[ inCohIndex ] += params['dotSpeedUnits']*numpy.sin( dTheta )
th[ inCohIndex ], r[ inCohIndex ] = cart2pol( X[ inCohIndex ], Y[ inCohIndex ], units ='rad' )
# Normalize Cartesian and Polar coordinates
# X, Y = pol2cart(th, r, units='rad')
elif params['moveMode'] == 'rotation-eq-angle':
# Coherent
th[ params['cohIndex'] ] += params['dotSpeedUnits']
X[ params['cohIndex'] ], Y[ params['cohIndex'] ] = pol2cart(th[ params['cohIndex'] ], r[ params['cohIndex'] ], units='rad')
# Incoherent
if params['nDots'] > params['nCoherent']:
inCohIndex = numpy.invert( params['cohIndex'] )
dTheta = numpy.random.rand(params['nDots']-params['nCoherent'])*numpy.pi*2.0
X[ inCohIndex ] += params['dotSpeedUnits']*numpy.cos( dTheta )
Y[ inCohIndex ] += params['dotSpeedUnits']*numpy.sin( dTheta )
th[ inCohIndex ], r[ inCohIndex ] = cart2pol( X[ inCohIndex ], Y[ inCohIndex ], units ='rad' )
elif params['moveMode'] == 'rotation-eq-spd':
# Coherent
X[ params['cohIndex'] ] += params['dotSpeedUnits']*numpy.sin( numpy.pi - th[ params['cohIndex'] ] )
Y[ params['cohIndex'] ] += params['dotSpeedUnits']*numpy.cos( numpy.pi - th[ params['cohIndex'] ] )
th[ params['cohIndex'] ], r[ params['cohIndex'] ] = cart2pol( X[ params['cohIndex'] ], Y[ params['cohIndex'] ], units ='rad' )
# Incoherent
if params['nDots'] > params['nCoherent']:
inCohIndex = numpy.invert( params['cohIndex'] )
dTheta = numpy.random.rand(params['nDots']-params['nCoherent'])*numpy.pi*2.0
X[ inCohIndex ] += params['dotSpeedUnits']*numpy.cos( dTheta )
Y[ inCohIndex ] += params['dotSpeedUnits']*numpy.sin( dTheta )
th[ inCohIndex ], r[ inCohIndex ] = cart2pol( X[ inCohIndex ], Y[ inCohIndex ], units ='rad' )
elif params['moveMode'] == 'laminar':
# Coherent
X[ params['cohIndex'] ] += params['dotSpeedUnits']*numpy.cos( params['laminarDirRads'] )
Y[ params['cohIndex'] ] += params['dotSpeedUnits']*numpy.sin( params['laminarDirRads'] )
th[ params['cohIndex'] ], r[ params['cohIndex'] ] = cart2pol( X[ params['cohIndex'] ], Y[ params['cohIndex'] ], units ='rad' )
# Incoherent
if params['nDots'] > params['nCoherent']:
inCohIndex = numpy.invert( params['cohIndex'] )
dTheta = numpy.random.rand(params['nDots']-params['nCoherent'])*numpy.pi*2.0
X[ inCohIndex ] += params['dotSpeedUnits']*numpy.cos( dTheta )
Y[ inCohIndex ] += params['dotSpeedUnits']*numpy.sin( dTheta )
th[ inCohIndex ], r[ inCohIndex ] = cart2pol( X[ inCohIndex ], Y[ inCohIndex ], units ='rad' )
elif params['moveMode'] == 'random':
dTheta = numpy.random.rand(params['nDots'])*numpy.pi*2.0
X += params['dotSpeedUnits']*numpy.cos( dTheta )
Y += params['dotSpeedUnits']*numpy.sin( dTheta )
th, r = cart2pol( X, Y, units ='rad' )
# end if moveMode
return r, th, X, Y
def dots_update_wrap(dotsX, dotsY, dotSpeed=dotSpeed):
# convert to polar coordinates
dotsTheta, dotsRadius = cart2pol(dotsX, dotsY)
# update radius
dotsRadius = (dotsRadius + dotSpeed)
# prepare array for dots that will die from falling out
lgcOutFieldDots = np.zeros(len(dotsTheta), dtype='bool')
# decide which dots fall out during expansion
if dotSpeed > 0:
# create lgc for elems where radius too large (expansion)
lgcOutFieldDots = (dotsRadius >= FieldSizeRadius)
# how many dots should go in area A?
numDotsAreaA = np.sum(
np.random.choice(np.arange(2),
p=[1 - pAexp, pAexp],
size=np.sum(lgcOutFieldDots)))
# get logical for area A
lgcAdots = np.zeros(len(dotsTheta), dtype='bool')
lgcAdots[np.where(lgcOutFieldDots)[0][:numDotsAreaA]] = True
# calculate new radius for dots appearing in region A
dotsRadius[lgcAdots] = innerBorder * np.sqrt(
(np.square(alphaExp) - 1) * np.random.rand(sum(lgcAdots)) + 1)
# get logical for area B
lgcBdots = np.zeros(len(dotsTheta), dtype='bool')
lgcBdots[np.where(lgcOutFieldDots)[0][numDotsAreaA:]] = True
# calculate new radius for dots appearing in region B
dotsRadius[lgcBdots] = np.sqrt(
(np.square(FieldSizeRadius) - np.square(alphaExp) *
np.square(innerBorder)) * np.random.rand(sum(lgcBdots)) +
np.square(alphaExp) * np.square(innerBorder))
# decide which dots fall out during contraction
elif dotSpeed < 0:
# create lgc for elems where radius too small (contraction)
lgcOutFieldDots = (dotsRadius <= innerBorder)
# how many dots should go in area A?
numDotsAreaA = np.sum(
np.random.choice(np.arange(2),
p=[1 - pAcontr, pAcontr],
size=np.sum(lgcOutFieldDots)))
# get logical for area A
lgcAdots = np.zeros(len(dotsTheta), dtype='bool')
lgcAdots[np.where(lgcOutFieldDots)[0][:numDotsAreaA]] = True
# calculate new radius for dots appearing in region A
dotsRadius[lgcAdots] = Scontr * np.sqrt(
(np.square(alphaContr) - 1) * np.random.rand(sum(lgcAdots)) + 1)
# get logical for area B
lgcBdots = np.zeros(len(dotsTheta), dtype='bool')
lgcBdots[np.where(lgcOutFieldDots)[0][numDotsAreaA:]] = True
# calculate new radius for dots appearing in region B
dotsRadius[lgcBdots] = np.sqrt(
(np.square(Scontr) - np.square(innerBorder)) *
np.random.rand(sum(lgcBdots)) + np.square(innerBorder))
# calculate new angle for all dots that died (from age or falling)
dotsTheta[lgcOutFieldDots] = np.random.uniform(0, 360,
sum(lgcOutFieldDots))
# convert from polar to Cartesian
dotsX, dotsY = pol2cart(dotsTheta, dotsRadius)
return dotsX, dotsY