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| Generating patternsTopographica provides comprehensive support for creating two-dimensional patterns of various sorts. These patterns can be used for generating training or testing inputs, generating initial or fixed weight patterns, neighborhood kernels, or any similar application. Simple patternsThe basic types of patterns supported by Topographica include: 
These patterns are created using objects of type PatternGenerator, which is an object that will return a 2D pattern when it is called as a function. For instance, the Gaussian PatternGenerator will return Gaussian-shaped patterns: $ ./topographica -g Topographica> from topo.patterns.basic import Gaussian Topographica> pg=Gaussian(xdensity=60,ydensity=60,size=0.3,aspect_ratio=1.0) Topographica> Topographica> from topo.commands.pylabplots import * Topographica> matrixplot(pg()) Topographica> matrixplot(pg(size=0.5))  
As you can see, the parameters of a PatternGenerator can be set up when you create the object, or they can be supplied when you generate the pattern. Any parameter not supplied in either location inherits the default value set for it in that PatternGenerator class. The reason for the name PatternGenerator is that the objects can each actually return an infinite number of different patterns, if any of the parameters are set to Dynamic values. For instance, a Gaussian input pattern can be specified to have a random orientation and (x,y) location:
$ ./topographica -g
Topographica> from topo.patterns.basic import Gaussian
Topographica> from topo.base.parameterclasses import DynamicNumber
Topographica> from topo.misc.numbergenerators import UniformRandom
Topographica> input_pattern = Gaussian(size=0.08, aspect_ratio=4,
xdensity=60,ydensity=60,
x=DynamicNumber(UniformRandom(lbound=-0.5,ubound=0.5,seed=12)),
y=DynamicNumber(UniformRandom(lbound=-0.5,ubound=0.5,seed=34)),
orientation=DynamicNumber(UniformRandom(lbound=-pi,ubound=pi,seed=56)))
Topographica> matrixplot(input_pattern())
Topographica> matrixplot(input_pattern())
 
There are many other types of patterns available already defined in the topo/patterns directory, and adding new patterns is straightforward. Just find one from that directory to use as a starting point, then copy it to a new file, modify it, and put the new file in the patterns directory. The new pattern should then show up in the Test Pattern window of the GUI automatically, and can be used in scripts the same way. Composite patternsOften, rather than writing a new PatternGenerator class, you can combine existing PatternGenerators to make a new pattern. To do this, Topographica provides the special Composite PatternGenerator, which accepts a list of other PatternGenerators and an operator for combining them. For instance, you can make connection weights be random but with a Gaussian falloff in strength by setting:
CFProjection.weights_generator=topo.patterns.basic.Composite(
generators=[topo.patterns.random.UniformRandom(),
topo.patterns.basic.Gaussian(aspect_ratio=1.0,size=0.2)],
operator=numpy.multiply)
More complex patterns can be created by combining multiple Composite PatternGenerators: $ ./topographica -g Topographica> from topo.patterns.basic import SineGrating, Disk, Composite Topographica> import numpy Topographica> surroundsine = SineGrating(frequency=8.0,orientation=0.25*pi, phase=3*pi/2) Topographica> centersine = SineGrating(frequency=8.0,orientation=0.60*pi) Topographica> centerdisk = Disk(aspect_ratio=1.0, size=0.35, smoothing=0.005) Topographica> surrounddisk = Disk(aspect_ratio=1.0, size=0.90, smoothing=0.005) Topographica> surroundring = Composite(generators=[surrounddisk,centerdisk], Topographica> operator=numpy.subtract) Topographica> center = Composite(generators=[centersine,centerdisk], Topographica> operator=numpy.multiply) Topographica> surround = Composite(generators=[surroundsine,surroundring], Topographica> operator=numpy.multiply) Topographica> centersurround = Composite(generators=[center,surround], Topographica> operator=numpy.add, Topographica> xdensity=160,ydensity=160) Topographica> matrixplot(centersurround()) 
Once created, even very complex composite patterns can be scaled, rotated, and placed together as a unit: $ ./topographica -g Topographica> from topo.patterns.basic import Gaussian, Disk, Composite Topographica> import numpy Topographica> Disk.smoothing=0.005 Topographica> lefteye = Disk( aspect_ratio=0.7, x=0.04, y=0.10, size=0.08, scale=1.00) Topographica> leftpupil = Disk( aspect_ratio=1.0, x=0.03, y=0.08, size=0.04, scale=-1.6) Topographica> righteye = Disk( aspect_ratio=0.7, x=0.04, y=-0.1, size=0.08, scale=1.00) Topographica> rightpupil = Disk( aspect_ratio=1.0, x=0.03, y=-0.08,size=0.04, scale=-1.6) Topographica> nose = Gaussian(aspect_ratio=0.8, x=-0.1, y=0.00, size=0.04, scale=-0.5) Topographica> mouth = Gaussian(aspect_ratio=0.8, x=-0.2, y=0.00, size=0.06, scale=-0.8) Topographica> head = Disk( aspect_ratio=1.5, x=-0.02,y=0.00, size=0.40, scale=0.70) Topographica> pg=Composite(generators=[lefteye,leftpupil,righteye,rightpupil,nose,mouth,head], Topographica> operator=numpy.add,xdensity=160,ydensity=160) Topographica> matrixplot(pg(orientation=pi/1.8, x=0.2, y=0.1, offset=0.5, size=0.75)) 
A wide variety of operators are provided for combining the patterns; see the
Composite parameter Selector patternsInstead of combining the patterns, it can also be useful to choose one from a set of different patterns, such as choosing randomly from a database of natural images. This can be done with the Selector PatternGenerator. As a contrived example, weights can be choosen at random from a set of four different pattern generators:
CFProjection.weights_generator=topo.patterns.basic.Selector(generators=[
topo.patterns.basic.Gaussian(orientation=DynamicNumber(
UniformRandom(lbound=-pi,ubound=pi,seed=99))),
topo.patterns.basic.Gaussian(aspect_ratio=1.0,
x=DynamicNumber(UniformRandom(lbound=-0.2,ubound=0.2,seed=12)),
y=DynamicNumber(UniformRandom(lbound=-0.2,ubound=0.2,seed=34))),
topo.patterns.basic.Rectangle(size=0.3,orientation=DynamicNumber(
UniformRandom(lbound=-pi,ubound=pi,seed=99))),
topo.patterns.basic.Disk(size=0.2)])
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